I do not think it would stop her from getting the nomination, but it might cost her votes among the more culturally conservative (relatively speaking) portions of the Democrat coalition, blacks, union members, and Hispanics.
However, it would probably kill her chances of winning the General Election. I do not see how a lesbian presidential candidate could get 270 Electoral votes.
Do the math, she will win in the liberal Northeast, but by reduced margins, she will also win California, but Pennsylvania, Ohio, and the whole of the South and West will go Republican.
It would be a wonderful spectacle because the party inner circle would be desperate to dump her in order to try to win the general election, but their “base” would never put up with an overt effort to say “our lesbian witch can’t win, let’s nominate someone who can!” It would be great fun to watch the Demagogues struggle in public with such a dilemma.
She would be happy if she got 269.