So far every idol I've attempted to flirt with has resulted in being informed that they are not into women. So I'm curious what the distribution is like. And is there any way to sus this type of thing out without your friendship points getting dunked?

Im not sure about exact proportions, but what I can say is that I have 5 idols on my group, and, out of those, only one is into girls (not sure if homo or bisexual). There is a way to figure out your idols' sexualities by messing with your save files. It's as easy as opening on a text editor and looking up 'Sexuality'. It'll reveal your idols' sexual preferences and allow you to change them if you wish to do so.

When you're playing a female manager the rate is close to 50% (including bi idols), so it shouldn't be too hard