The question requires some determinations or clarifications. The context in which I'm asking the question, apart from the contemporary world, is the claim of the Catholic Church, following Thomas Aquinas, that: even God can not make a triangle with angles not equal to two Right Angles. (This is part of the definition of the technical term "omnipotence".)
I'm going to try to ask some Catholics this question too. When one brings in the non-euclidean, one makes an appeal, it seems, to shapes that are not available to the senses. For that reason even though men were always able to make such a geometry, until maths were used in the modern way, for predictive physical modeling, they were not developed until quite recent times, the Enlightenment.
In one sense, one says, any geometry is true, the Euclidean is true, and can never be "disproved", but this is said with respect to the formal character of geometry. Not to the shapes as they are for the senses, abstractly represented by the so-called universals or perfect abstractions, of a geometry. If geometry refers to real shapes, in the world, and if the Thomistic decretal, as it were, is taken to speak to the limits of God's will, that it is limited by the order of nature, and that what is said in the statement about the sum of the angles is false, does it not suggest there is no order? I.e., because if the non-euclidean corresponds to something, in that order, is it not, in a certain sense limitless, and never truly subsumable under the statements of a geometry? Thus, in any serious sense there is no order to speak of. One would always find more.
Are there real shapes corresponding to the non-euclidean maths? I.e., real but not available directly to the senses? Ergo, does God's order, in the Thomistic sense, go beyond the senses towards absolute and unruly, if you like, variegation?
Is the statement about the triangle that is Euclidean genuinely made false, in the case that, it refers to the order of the world, of the visible things? Where the visible things, being extended beyond man's current sense-capability, include real triangles that don't fit the "two-right-angle" criteria.
I am not sure one can get away with saying that the Triangle refers only to the abstraction, or the idea of the triangle. I would think Thomists might argue that, but I wonder if that would be false, since the reason for not developing non-euclidean geometries was not lack of skill or imagination, but because of the belief that one should stay with the visible world, Aristotle, the great influence of Thomas, holds sight to be the most valuble and pleasurable of the senses.
Let those who answer answer in their own fashion, according to the way they understand the question. In the interest of pouring some light on the general subject.