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?
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.
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.