You are speaking of the sensual universe as the ‘Real’ or the ‘Truth’. The question is something which underlies a tremendous amount of philosophical speculation. First, to ask if reality changes because most or all people believe that the world is flat, does not make it true, does not change the truth...we all see the sky as blue and spherical, but does that mean that air is blue or spherical?? A thing may be experienced but that does not make it real, even if it is a perception shared by all. We all do not see x-rays, does that mean they don’t exist? Do not people die from radiation exposure, smoking cigarettes, etc., etc, whether they believe in, or understand it or not? If a number of people are standing in a desert and see a mirage, does that mean the mirage is real?
There is a ‘Reality’ which exists beyond our individual perceptions. In the Advaita Vedanta (non-dual Hinduism), the sensual universe, the phenomenal world, that we perceive is not the ‘Reality’. It is referred to as ‘adhyasa’ or superimposition. We superimpose an illusion on the Ultimate Reality. There is a relative reality, relative truths, that exist, that we share in common, as we have all have defined similar senses and similarly constructed nervous systems and brains. But our perception of the ‘Reality’ is through colored glasses so to speak. Professor Chandradhar Sharma says in his book The Advaita Tradition in Indian Philosophy (pp170-1):
Illusions may be perceptual or non-perceptual. Perceptual illusions, again, may be conditioned by some media (sopadhika) or may not be so conditioned (nirupadhika). The former include the optical illusions of reflection, like the reflected image of a mirror or water, and of refraction, like a straight stick appearing bent in water, colour-illusions; and illusion of size, distance, etc. These illusions are called 'normal', as they are shared by many percipients and continue to persist even after their falsity is known and lead to what is called 'veridical perception'. The wold illusion is more like these. But a subjective factor is definitely involved in these and a person who knows their falsity is no more under illusion even though he may continue to see them in the same way. The latter type of illusions which are not conditioned my media are the illusions of rope-snake, shell-silver, etc., and also include dream-objects and hallucinations. These vanish for good when their ground is known. The non-perceptual illusions include wrong opinions, beliefs, dogmas etc.which pretend to be true, but on critical inquiry are found to be false. These are more dangerous and include what Bacon has called Idola, Tribus, Idola Theatri, Idola Specus, and Idola Fori. An illusion, therefore, is wrong knowledge or belief which is due to the super-imposition of the unreal on the real and is set aside subsequently by knowledge of the real.
For realism the fact of illusion has always been a hard nut to crack. No form of realism whether Indian or Western has been able to satisfactorily explain illusion. Realism believes that the perceived content is entirely independent of the act of perception. Knowledge merely represents; it does not construct. It cannot make or unmake things. The object is in no way affected by by its knowledge; it gains or loses nothing by being known. Knowledge merely represents the given without affecting its nature. Now the problem is this: If knowledge never misrepresents its object, how can error arise?...
Our minds and our senses interpret the Reality according to their abilities. In the section titled Adyhyasa or Superimposition, Swami Vireswarananda writes on his interpretation of Sankara’s chapter of the same title (https://www.wisdomlib.org/hinduism/book/brahma-sutras/d/doc62758.html):
The question then naturally arises : If Truth is one, whence arises this many which we experience through the senses ? Truth cannot contradict experience. So Sankara had to explain this apparent contradiction between Truth and our everyday experience. He says that this plurality is an illusion (Mâyâ). It has no reality, for it disappears when the knowledge of the true nature of Brahman is realized. It is just like seeing a snake in a rope in the dark. This wrong perception is brought about by ignorance (Avidyâ), which is beginningless. It is this ignorance which is the cause of all this duality, Brahman [the Absolute Existence, Absolute Consciousness, but not a personal God or Being] being mistaken for the world. On account of this ignorance the individual soul identifies itself with its adjuncts (Upâdhis) viz. the body, senses, etc., which are only superimposed on it. This identification makes the soul think that it is the doer, enjoyer, etc.—though the truth is that it is none of these—and thereby it comes under the sway of birth, death, happiness, misery, etc., in short, becomes bound down to this world (Samsâra).
When Sankara says that the world is false, he does not mean that it is absolutely nothing, but that our experience is liable to be stultified by means of knowledge of things as they are. The world has a relative existence; it is true for the time being, but disappears when true knowledge dawns. It is not real for all times, in other words, it is not real from the absolute standpoint. Mâyâ or ignorance is not a real entity. We can neither say that it exists nor that it does not exist. It is a mystery which is beyond our understanding; it is unspeakable (Anir-vachaniya). As Maya is not real, it cannot be related to Brahman, the Reality, in any way whatsoever; for any relation between truth and falsehood is impossible. The relation is only apparent, and therefore Brahman is in no way affected by this illusion which is superimposed upon It, even as the rope is not affected by the snake that is assumed to exist in it.
… Sankara’s explanation of the world as an illusion has given his philosophy the name of Mâyâvâda or Anirvachaniya Khyâtivâda. It is also known as Vivartavâda, the doctrine of the apparent modification of Brahman into this phenomenal world, as opposed to Parinâmavâda or the doctrine of the actual modification of Brahman into this phenomenal world, as held by some other schools of Vedânta like the Visishtâdvaitavâda of Râmânuja.
Sankara anticipated that this method of explaining the phenomenal world would raise a protest from the various other schools of his time. So at the beginning of his commentary on the Brahma-Sutras, he writes a masterly introduction, which is well known as the Adhyâsa Bhâshya or the section dealing with superimposition, wherein he establishes superimposition as a statement of fact and not a mere hypothesis. He starts with the objections that can possibly be raised against his theory of superimposition and then refutes them. He says : It is well known that the subject and the object, which have for their spheres or contents the notions of ‘I’ and ‘Thou’ respectively, and which are opposed to each other as darkness and light, cannot be identified. Hence their attributes also cannot be identified. Consequently the superimposition of the object and its attributes on the subject, whose essence is pure intelligence, and vice versa, ought to be a logical impossibility.
If the world phenomena are a case of superimposition, like the snake in the rope, then which is superimposed on which ? Is the world superimposed on Brahman, or is it the reverse? In the latter case, the world, which is the substratum, like the rope in the example, would be a reality. If it is the other way—the world on Brahman—it is not possible, for Brahman is not an object which can be perceived by the senses like the rope. A thing becomes an object when it is limited by time, space, and causation. Since Brahman is unlimited, It is beyond these, and so cannot be an object of perception ; as such It cannot be the substratum of a superimposition. Brahman is also the inner Self of everyone and therefore can never be separate and in front of a person like a rope, when alone the world can be superimposed on It.
Neither can Brahman be both subject and object of the thinking process, for one and the same being cannot both be the agent and the object of its activity at the same time. An object is that on which is concentrated the activity of the agent, and hence it must be different from the agent. If, again, Brahman is manifested by some other knowledge and thus becomes an object, It ceases to be self-luminous and becomes limited, and this the scriptures do not accept. Further, in all cases of superimposition there is an antecedent real knowledge of the object which is superimposed, as of the snake in the example. So to superimpose the world on Brahman a real knowledge of the world is necessary, and this would make the world a reality, with the result that the cessation of the world phenomena would be an impossibility and Liberation would be impossible. Thus in whatever way we may try to establish the theory of superimposition, we are not able to do so.
Yet, says Sankara, it is natural (a self-evident fact) on the part of man, because of ignorance, not to distinguish between the two entities (the subject and the object), which are quite contradictory, and to superimpose the one on the other, and their attributes as well, and thus mixing up the real and the unreal to use such phrases as “That is I”, or “This is mine”. The Self again is not altogether a non-object, for it is the object of the notion of the Ego. The Self does not entirely elude our grasp. Though the inner Self is not an object and is also without parts, yet owing to ignorance, which is unspeakable and without a beginning, attributes like mind, body, senses, etc., which are products of ignorance, are superimposed on the Self, and it behaves as if it were an agent, enjoyer, possessed of parts, and many—although in truth it is none of these—and thus becomes an object. The real Self can never be an object of knowledge. Self-consciousness is possible only with respect to a Self already qualified by these adjuncts (Upâdhis). This sounds like an argument in a circle; for to establish superimposition we have to accept the Self to be an object, and the Self can be an object only through the superimposition of adjuncts (Upâdhis); it is actually not so. It is a case like the seed and the tree. The seed gives rise to the tree, which again produces the seed, the cause of the future tree, and so on. So in this series of illusions without a beginning, the Self, which is the substratum of the present superimposition, is an object on account of a past superimposition, and that one had for its substratum the Self, which had become an object of a still earlier superimposition, and so on ad infinitum . The pure Self without the limiting adjuncts is never the substratum of a super-imposition. It is the difference in the limiting adjuncts, as shown above, that makes it possible for the Self to be at the same time an agent and the object of action.
Superimposition, again, is due to ignorance and hence it is not necessary that the knowledge of the object superimposed must be a real knowledge. It is enough if we have a knowledge; it need not necessarily be real; it can itself be another illusory knowledge. That the Self exists is proved by the intuitive knowledge we have of it. This is well known and but for it nothing would have been cognized in this world. “He shining, everything else shines” (Kath. 2.2.15). We know things in and through it; 110 consciousness or experience is possible independently of it. Everyone is conscious of his own Self, for no one thinks, “I am not”. Nor, again, is it necessary that the object to be a substratum of a superimposition should be before us, for we see that Âkâsa (sky), which is not visible to the senses, becomes a substratum for superimpositions by the ignorant, who impute blueness, spherical shape, etc., to it in such expressions as, “The sky is blue”, and “It is spherical”. Thus superimposition is an established fact.
Thus, when we speak of the relative world, the relative universe, it is a relative truth, not the Absolute Truth. There is an Absolute Truth, Reality, that exists as the substratum of this world, but we do not perceive it. Neither does a group misperception define either the Absolute Reality or the relative reality.
Another reference for the above is A Critical Survey of Indian Philosophy, section X, Maya and Brahman, available here - https://archive.org/details/IndianPhilosophyACriticalSurvey
