It's more like if he introduced himself as being a young child or a dog. No-one should be under any obligation to play along with Bob's claims to be an infant or a canine when he is neither.

By the same logic as you are presenting, it is toxic and hostile to impose this ideology upon others. If believers of this ideology want to use "preferred pronouns" and such, they should of course be free to do so.

But others who do not hold this ideological stance, including those who oppose it for whatever reason (e.g. because they see the concept and implementation of "gender identity" as fundamentally sexist), shouldn't be forced to pay lip service to it, any more than atheists should be forced to pray at work.

You call this refusal "assholery", but presumably that is because you are a believer of this ideology - including the belief that to reject it is "transphobic" (which is roughly equivalent to the religious zealots' cry of "heretic") and therefore, per this belief, reprehensible?

Yes, of course. If you believe that false claims of an opposite-sex identity constitute a harmful lie, why should you be compelled to endorse it?