I was considering that if I were in some lawmaking position I would consider advocating that abortion rights should be voted on by females and the result of that election would become law.

On philosophical and ethical grounds it makes sense to me. Whereas on most issues it would seem wrong to only allow a special interest group to vote, because the issue affects everyone in society, it does also seem like there are sometimes social phenomena that are only relevant to a specific class of human. Laws are generally meant to prohibit immoral actions as well as improve society out of a collective obligation for everyone to equally contribute to that end. It makes sense that if a law only would affect the quality of life of a specific group, with limited ramifications for people outside that group; and since democracy is basically just meant to be a census, an average, of what people want for themselves, where the majority rules; that you could create sub-group specific elections. For example, residents of one state cannot vote in the elections of a different state, I believe.

Is it legally possible to create a group-specific vote? If lawmakers proposed a referendum, sort of like Brexit, with the clause that only women would vote, and that the result would become enacted, could lawmakers or citizens vote such a referendum into existence, or would it be struck down as unconstitutional?