LGBT

But women rabbis do exist, so they're obviously being trained and ordained somewhere.

I am not up to date in my knowledge of the various branches of Judaism, but I know some are more conservative and others are less so.

In any case, an orthodox yeshiva ordaining an out gay man sounds like a pretty big deal to me. Mazel tov to Rabbi Tadhg Cleary and to Yeshivat Chovevei Torah for ordaining him!