Maybe the egalitarian-minded Catholics should just become Episcopalian, or maybe Lutheran.
I know many magisterial Protestants in the US like to advertise their churches as "Catholicism without the sex discrimination", but that isn't actually the case, and it's insulting to the memory of the seminal figures of Anglican and Lutheran history to suggest that that's all those traditions boil down to.
I didn't say that.
Perhaps I should have just said any tradition egalitarian Catholics might prefer. I just mentioned those two since they contain the high church familiarity, but that's not necessarily what's important to them. They can be whatever they want, and maybe they could find something in different denomination that appeals to them.