My AGAB is important to me because the way I was raised has shaped my experiences and personality. Although I am transitioning, I identify more with the AFAB experience in certain ways, so there are certain things I feel more comfortable bonding over with AFAB people. I'm also new to transitioning, so I am very curious about others' experiences.
I do respect the views of people who don't want to identify at all with their AGAB, and it's perfectly ok to say that you don't want to share that information if people ask. I appreciate the tip to ask about hormones instead, and I'll try to do that in the future in order to be more respectful.
There's no universal experience, but it's more like an umbrella term, a sort of fundamental experience that most can relate to. I personally don't believe my experience to be wildly different from that of cis women, other than that I have also suffered from dysphoria. I typically identify even more closely with transmasc people. It is ok to disagree with me, but I do believe our upbringing and experiences shape our personalities, and that if I was socialized male from birth that I would have different experiences, thus a somewhat different personality.