> you can admit to yourself that you are attracted to a variety of genders without thinking of yourself as being queer.
Sure, I can think of myself as bisexual instead, which I do. (tongue in cheek)
I can't speak for anyone else, but for me, bisexuality can't not be part of my identity. Like @eyelidlessness, it took a long time to come to the conclusion. It affects how others see me, how they treat me, if they'll date me, etc. It caused heartbreak, depression, and so on. These are all experiences that set me apart from most other people, whether I want them to or not. If that's not identity, I don't know what is. As one ages and settles down, these things can become less central to your identity, but they're still there and important. Stoicism is one thing, but dismissing the difficulties experienced when going against the grain in any area of life is wishful thinking.
I think Paul Graham could have gone one step further in his analysis. Identity is the combination of labels, community and emotion. Labels are very valuable tools as shortcuts in discussions. They can also lead to dissonance, when definitions don't align or context is missing.
The community aspect, especially in rainbow or mental health issues (not an exhaustive list), can be critical to well-being and survival. Could you find the same support network somewhere else? Yes, and plenty of people do, but that doesn't discount the value of the Pride movement or the Trevor project, for instance. The downside of community is it can evoke tribalistic tendencies.
What Graham seems to take issue with most is the emotional component of one's identity. What's relevant here is not whether you have emotions about your identity, but whether you can set them aside long enough to have a dispassionate discussion. It does require that participants have a healthy emotional baseline, are mature enough not to take everything personally and retain an open mind.
I feel it's also important to point out that there is a difference between having an identity and being an identitarian. You can be bisexual without being an activist. You can be an activist without going full woke and thinking of every interaction as power balances and oppression dynamics.
We can choose whether it becomes a central part of our lives, whether we need to surround ourselves with only like-minded people or whether we enter into discussions looking to be offended, be right or exchange ideas. In that sense, it's no different from having a political opinion, a profession, musical tastes, a hobby or anything else.