I agree. This idea about what gender is (a feeling, a self perception, a set of characteristics, whatever) is a social construct. Sex, otoh, is not a social construct. It's not a belief. It can be objectively demonstrated to be real. Reality matters more to me than beliefs, feelings and ideology. I do think it's necessary to make a choice as to what is most important to you, just in order to live with integrity and consistency in your values.
Lots of people believe in God as well, and God is also just a social construct. As long as believers know that, they are living in reality. When they lose sight of that it leads to intolerance to perfectly harmless differing points of view.
I'm good with those who believe in gender, in God, in whatever they like. I'm just not good with them imposing their beliefs on non-believers. That's why I strongly object to any laws about "misgendering." It's the equivalent of making it illegal to say there is no God. So that's where I'm coming from. I respect your right to believe that this thing you call gender matters. I do not think it is right to label non-believers as bigots, hateful, phobic, etcetera. If they make truly hateful, inaccurate, dehumanizing generalizations about the people involved, I would agree that that shows bigotry. But saying gender, (as a feeling, self perception, set of characteristics) is meaningless is not inherently hateful. It's often just that the person has chosen that what can be demonstrated to be real is more important.
I hope that makes sense and doesn't just look like a word salad ramble. It's a bit difficult to put it into words.