I’d say that this is a bit different situation than the once-proposed #anti-semitic. In that case the vast, vast majority of the time, anything which is anti-Semitic is also racist and/or conspiracist (and usually both), making it not entirely redundant (as not all racism or conspiracy theories are anti-Semitic in nature) but still mostly superfluous. There’s also the factor that the #racist tag covers all forms of race-based and ethnicity-based bigotry, so it’s questionable whether we should single out one form in particular, even if it’s a particularly common one.
In this case, all of the heterophobic ones which I can recall have so far been covered by #sexist, due to sexism against men and usually women as well. It’s hard to imagine any which would not technically be covered by that, or #crackpot plus #psycho. But unlike #racist, we don’t have a catchall #sexual_orientation_phobia, and sexual orientation *is* not only a major component to heterophobia but also the most relevant one in most cases. There might occasionally be ones where any sexism is only a minor or indirect component to it and #sexist isn’t necessarily needed, as #heterophobia covers it just fine by itself.
I’m not saying “yes, we should” to either of them (I’m neutral on both) only that a #heterophobia tag seems to have a bit stronger argument going for it.