There are not a lot of “equal rights/#metoo” cases coming before the court. None of the cases currently scheduled for the Supreme Court have anything to do with that, and rarely would such a case make it there as those deal with state level criminal law.
In any event, thats not a basis for recusal in the first place—”prebias” is not a thing, and having some personal involvement in a type or class of case does not require recusal. Having a close personal connection to a litigant or other person involved (the defendant is judge’s son, the CEO of the plaintiff company is judge’s cousin), or having a personal interest in the outcome of a particular case (judge has heavy investments in defendant’s company)...those are the types of things that demand recusal.
I use the “metoo” term as kind of a broad way of expressing the kinds of women’s rights cases that are always in the federal court pipeline, some of which will always get to the supreme court. No I didn’t go thru the whole federal court data base but I’ll bet there are a few such cases percolating now; there always are!