We all have an identity - a sense of who we are and what makes us similar and different to others. Everyone has views on the self perceptions / identities of others (eg she thinks she is a bad mum but I think she's a great mum, he thinks and acts like he's an Adonis but no one I know thinks he's remotely attractive etc).
Identity is multifaceted and made up of many components. GCs tend to have identities where gender norms don't feature, or where they do, these are about being gender non conforming. Many people aren't aware whether or how gender norms play in to their identities. Men who think of themselves as 'alpha' and women who think of themselves as 'girly' arguably have gendered ideas forming a significant component of their identities.
Transgender people, by definition, place ideas about gender as a central component of their identity. Thinking of oneself as being masculine, feminine, or neither shouldn't be a problem for anyone other than those who want to uphold/ sustain gender norms.
I am not sure why TRAs expect us to revere gendered components of people's identities and not have views on them as we do with all other components of identity.
I think that how we address issues linked to differences in a person's identity and how we perceive them is often complex territory (e.g the company an employee works for and the employee disagreeing over whether they are 'great with people', and meeting someone at a busy party who thinks they are 'really interesting' and you don't). We can often avoid needing to confront people about aspects of their identity we don't agree with, but this often isn't the case with those with transgender identities. Despite what TRAs say, I don't think this is any more or less upsetting than being challenged on other primary components of one's identity.
Many GC people have identities where ideas about justice, fairness and equality are central to their self perception. Being called / seen as bigoted is deeply upsetting/ infuriating. This is layered with additional emotion that comes from knowing that bigots are ostracised within wider society, which threatens objective aspects of quality of life. This isn't dissimilar to trans people's experiences of being called/ seen as being different to their self perception.
I think we are getting closer to sanity around questioning the primacy of gender when it comes to issues relating to identity, I think we are also reaching more widespread recognition that not everything be considered a component of identity (e.g sex and age). I do think we are a long way off addressing issues linked to ideas about hierarchies of oppression. My prediction is that as long as people seek to pit oppressed group against each other, this will rumble on.