Is it the lack of belief that offends them, or the lack of willingness to pretend?
My guess is that it depends on the motivation of the individual that is offended.
Broadly speaking, my guess is that the self-serving acronym people get themselves to a point where they eventually don't care whether people believe, pretend or push back (all of it helps them feel like they've got power over people... part of the thrill), the genuinely dysphoric ones and non-binaries would assume that it's incorrect and incomprehensible that people wouldn't believe that we all have a gender identity/inner sense of gender (perhaps exacerbated by autism) and the vocally supportive "handmaiden" types don't want to let on that they worry about whether it really is something that they believe, being too busy trying to push away doubts to show how "educated" they are compared to the "ignorant GCs".
The acronym people seem to be split in to those that know they have it and those that don't. Presumably those that don't know just end up at the same point as those that do, where it really doesn't matter as long as they get what they need out of it.
All of this is solved by repeating the mantras and framing any "heretics" as refusers and ignorant. No critical thinking is required at this point, which probably provides a sense of relief that nobody will penetrate the belief with difficult questions. It's definitely a very good solution for any evangelical-type group that wants to keep people believing, whatever motivations are held by individuals within the group. It's also quite interesting that this exact same argument is thrown at "believers in gender critical ideology". That helps to shore up the gender identity belief defensive walls even more.
Obviously there are some exceptions where people know that their gender dysphoria is a mental health condition (e.g. Blaire White, Buck Angel), are happy to state this and will recognise their sex. But I'm assuming that they still have an inner voice telling them that they are in the wrong-sexed body, even if they don't recognise this as a belief in the idea that they have a gender identity.