Great editing @FlirtsWithRhinos
Yep, this really does show how close the different positions are when it comes to challenging the sex-based expectations that are placed on us from birth. There are many that we uphold within our own cultures every day without even realising it. For example when my first child was born I got lots of pink stuff and girly toys as gifts for her. As someone who doesn't believe in gender identity, I don't believe that sex is "assigned at birth". However, I do believe that there are a whole load of sex-based expectations placed on everyone right from the start. Sadly, as women we seem to have to fight a whole lot more to break out of these when we don't want to adhere to them.
For me (as an atheist) it's similar to how closely I find myself agreeing with many of the teachings in the bible. For example, the 10 commandments make sense to me as ways to be a decent person. I don't follow them as instructions or because I would be fearful of God's wrath if I didn't. I just happen to agree that they seem like a good way for people to live within a society. Equally, I disagree with much of what the Bible says, including some of the "instructions" on how to live.
If it's not recognised as a belief, that's where the harm comes in. Beliefs can be accommodated in our existing laws and ways of living as long as they are understood to be just that. Just as we're not mandating that everyone has to go to church on a Sunday, we shouldn't be mandating that transwomen belong in women's spaces and sports. Also we shouldn't be encouraging adolescents who are struggling with the huge emotional upheaval of puberty (for girls, much of this is linked to a realisation about what society expects because of their sex, particularly when it comes to how men view them sexually) to think about gender identity as a way to make sense of it.
People can believe in gender identity should they wish to. Equally, nobody can compel anyone to do so. What's more important IMO is to call out the harms that this belief brings with it (e.g. sterilisation of children, providing an opportunity window for predators to access children/women under the banner of inclusion) and to make sure that the way it's accommodated in society doesn't impact anyone else's boundaries.