> One can disagree with you and still believe you have the right to live how you like

You're missing the point. "Disagreement" implies some level of care. You can't claim to not give a fuck, and also claim to disagree. These two statements are incompatible.

Example: I disagree that trans people should be treated poorly and insulted. Therefore, I care that trans people are not treated poorly and insulted.

> Your first sentence doesn’t imply the second

Yes, it does. Passage as stated: "female gender refers to the social roles and norms associated with being a woman."

Letting A = "someone follows the social roles and norms associated with being a woman" and B = "someone has the female gender," the passage becomes:

Premise (definition): To have the female gender is to follow the social roles and norms associated with being a woman — so A implies B. Premise: This person follows those roles and norms (A). Conclusion: Therefore, this person has the female gender (B).

Symbolically: A → B, A, ∴ B — a straightforward modus ponens. I knew that my logic courses would eventually become useful. Just kidding, logic is always useful.

> As long as we agree that being an asshole shouldn’t be against the law then live your life.

I agree.

> For the record, this wasn’t an issue for me until the left made it a wedge issue

The left didn't make this a wedge issue. This is obvious; there is nothing for the left to gain from doing that. The left did the same dumb thing they always do: take a moral stance and then get kicked in the teeth by bad-faith polemicists who'd rather talk about bullshit that never happens to anyone but sounds kinda scary than about actual shit that actually happens and makes them look bad.