Great question!
You have three different concepts at play, and they don't quite overlap, so let's lay out what you have:
- IBE is an ontological strategy for arguing the existence of other minds.
- Phenomenal conservatism is an epistemological heuristic for justifying evidence of the existence of other minds.
- Theory of mind is a psychological explanation of how people function in their belief of other minds.
Note that these are slightly different domains of discourse, and therefore they are not in direct competition with each other as you seem to presume. Ontology is the philosophical discipline that rests on presumptions and arguments about the existence of minds. It is interested in the question 'Do minds exist?'. Epistemology is the philosophical discipline that revolves around belief and justification about the existence of minds, and therefore asks the quesitons 'How do we know minds exist?' Lastly, theory of mind is a psychological rather than logical explanation which purports to explain how is it that people believe minds exist even before they engage in logical theories of justification and explanation. Let's explore.
Children believe other minds exist long before they begin to construct arguments for and against and justify their conclusions. A young child will anticipate other minds and behave accordingly as any parent well knows, and young children are infamously natural lawyers attempting to persuade you of their innocence when they violate the rules. None of this happens without a presumption that those around them have minds. Just like a horse is essentially wired to come out of the womb and gallop around after a short period, a human baby quickly starts to manifest an intelligence in regards to socialization and interacting with other people. The job of the psychologist is to explain this observation scientifically. The explanation of theory of mind essentially lies in psychological, linguistic, and anatomical and physiological theory. This sort of psychological explanation is only philosophical if embraced from as a naturalized epistemological fact (SEP). While in the West, we often appeal to science as a philosophical tool, in fact, that is a deliberate choice, and not a metaphysically necessary one.
As for phenomenal conservatism, it turns out that contemporaneous work on reasoning and the philosophy of logic show that people rely heavily on intuition in reasoning, and are constrained by the nature of the brain in terms of how they go about constructing and using logic. One good example is the idea that human reason is inherently defeasible (SEP). The Laws of Logic aren't some universal fact that the mind receives and obeys, but rather that human brains construct and use logic as an extension of their linguistic prowess. Since the brain is limited, so too reason is limited, and all human thinking is fallible (IEP). As such, most reason is informal and non-deductive, and arguments are subject to new information such as defeaters. In the face of such an understanding of human reason as imperfect, it then becomes necessary to explain how human logic functions in the face of imperfection. One explanation is that human logic is heuristic, that is, uses rules of thumb to arrive at conclusions. Phenomenal conservatism might be seen, then, as an outgrowth of our tendency to arrive at the state of critical thinking with naive realism. In fact, here, psychologists use the term also albeit slightly differently. From WP:
In social psychology, naïve realism is the human tendency to believe that we see the world around us objectively, and that people who disagree with us must be uninformed, irrational, or biased.
Note how that differs from the WP article on the philosophical concept:
In philosophy of perception and epistemology, naïve realism (also known as direct realism, perceptual realism, or common sense realism) is the idea that the senses provide us with direct awareness of objects as they really are.
Note the former definition has overtones of psychological egocentrism built in, and the latter has overtones of philosophical realism built in.
Lastly, having an ontological argument using inference to best explanation is yet a third nuanced position in the philosophy of mind in that it attempts to start de novo with language to build an persuasive or perhaps irrefutable logical argument that minds exist. This isn't the same as presuming minds exist, but is an exercise in logic to show that metaphysically and logically more narrowly, minds do indeed exist according to some notion of 'existence'. Note, that the nature of existence itself is metaphysically contentious, and therefore unlike theory of mind which is a psychological fact based on observation that humans believe in minds without logical justification at all, and phenomenal conservatism which is the argument that humans have a heuristic they use to accept minds with some efforts of philosophical justification, an argument for the existence of mind that relies on IBE is a fully-fledged argument starting with first principles and drawing on a wide range of premises and inferences to attempt to show that disbelief in the mind is logically inconsistent.
So, now that we've adequately explicated the three notions, we are in a position to answer your question.
If I use arguments to justify my belief in the existence of other minds, do I have to abandon the theory of mind?
You cannot really abandon your theory of mind because it is native to how your mind works. The theory of theory of mind is a psychological explanation that explains in a third-person methodology why you believed in other minds long before you were capable of reasoning. Those intuitions are baked into the development of your brain by evolution to allow you to function socially long before you even can utter sentences. You can ignore those intuitions, or perhaps you can justify ignoring them with solipsism, or you might have a deficit in your intuition as it has been argued that autistic people might have, but you cannot simply stop your brain from having and using a theory of mind.
What you can do is strengthen your belief in other minds with an argument using IBE and appeal to the full canon of the philosophy of mind like Chalmers does, or you can argue that the mind doesn't exist and is illusory like Dennett does, and in doing so, you can invoke phenomenal conservatism as an explanation of how your mind does epistemology which is to suggest that if something appears to exist, your mind simply treats that as acceptable justification until positive evidence arises to the contrary (such as the realization that a mind is not a physical thing and therefore is not detectable by the senses directly).
So there's no need to chose among these, and in fact, arguably, this is typical for almost everyone. We are born into the world with a theory of mind that allows us to intuitively interact with other minds until we get to an age when we start critically thinking, and then if embrace philosophy and its methods, we then attempt starting with our metaphysical presuppositions to construct an persuasive and coherent argument that minds do in fact exist and that they operate according to principles such as conservatism.
