It's an "easier sell" of a different thing.
I'm not seeing a "we" forming here as far as "trans acceptance" is concerned.
Judging from your comment history, your perspective on this seems to basically be grounded in an objection to (more generously: apprehension about) transgender healthcare practices. On purportedly scientific grounds, while ascribing a "politically-driven" motivation in terms of groupthink to people who support these practices. So I think your motivation to ascribe this to a "cultural thing" is grounded in a desire to decouple it from the healthcare thing, because you think it serves an overall political project better.
I'm with you on loosening gender roles. I'm not with you on reducing trans acceptance to that.
> why are we doubling down on gender binaries and talking about switching genders instead of creating a campaign that would both get at the root of the issue and be easier to swallow for a larger portion of the country?
In my personal life, I am probably about as far from "doubling down on gender binaries" as anyone you are likely to encounter. In my experience, I find many more people who are genuinely working past "doubling down on gender binaries" in transgender spaces than I do outside them.
My not-doubling-down-on-gender-binaries approach to it is not an easy pill to swallow for a large portion of the country. It may not even be an easy pill to swallow for you. (E.g. "which" bathroom do you want me in? How easily do you think the rest of the country will swallow that?)