It's unfortunate he used his final days to reiterate his long-standing belief that trans rights, now an issue with 60%+ popular support, is a losing issue. That will always be a "but..." in any conversation about his legacy.
This article also shares polling that would indicate, counter to your point, that support isn't as cut and dry. Which, I believe would actually make a case for the approach he suggested in the recent interview?
It's the old "meet society where it is" vs "push society forward by supporting the thing" debate. His proposed granular approach didn't work for gay rights, and it hasn't for trans rights. It took things like ACT UP's more blunt approach to shift public opinion on gay equality.
The US tends to be conservative, so real change only comes when large numbers of people are forced to rethink their views. The Democratic party taking credit for big changes but never really pushing for them, or actively standing in the way, is one of the main criticisms of the party.
People broadly support transvestites and transsexuals not being discriminated against in scenarios like employment, access to housing, and so on. This approach to equality is analogous to what the gay rights movement achieved.
However the divisive issue is whether they should be treated as if they are the opposite sex in all contexts. This is a lot more unpopular, because it has the effect of harming and disadvantaging women and girls.
Turns out that most people don't appreciate the unilateral imposition of males on female-only spaces. Prisons, sports, locker/changing rooms, etc.