I haven't looked yet at the gemara this time around, just the mishnah...but the question occurred to me, if Bais Shammai gives Bais Hillel an offspring of tzaras habas (a mamzeres to Bais Hillel), are the ovair on lifnei iver? After the bas kol, certainly. What about before the bas kol?
What happens in a case where someone who holds it's assur to open bottles of soda gives a bottle of soda to open to someone who holds it's muttar?

I know my Rebbi, Rav Yisroel Belsky, held that it was Ussur. If you hold something is Ussur, how can you give him something to do. He has the same Chiyuv as you have and just like you cannot do it, he's not allowed to do it either. (If it's only a Chumra, since you hold Halachically you can do it, it's permitted to ask him.)

Even though he relies on the Heterim to do it, that's because he relies on those Heterim, which he's allowed to. But this is not a Din on the Gavra, that Issur depends on the person. The Halacha applies universally. If it's really Mutter it's Mutter to everyone, if it's Ussur it's Ussur to all. If you hold it's Ussur, it's Ussur to everyone as far as you are concerned and cannot help anyone to do it.

Would the same be l'hefuch, if you thought it's mutar, and he says it's assur, for example for bais Hillel to be mshadech tzaras erva (without chalitza) to bais Shamai?

Isn't that the Gemara on 14b that if the girl was not fitting for them they told the other.

They did inform them, and it is considered ahava and rayus that min hastam they could take wives, because if there was a problem they could count on being informed.
From the gemara it might seem that there is no lifnei iver, because if there was, what's the great shvach and ahava that they informed them?

You're right. But see Ritva that says that you cannot give someone something that the other thinks is Issur (brings a Raya from Gemara in Chulin) but over here you're not handing them the wives, but rather they're taking themselves. You don't have a Chiyuv to remove him from doing it, if not because he;s your friend and you cannot do to your friend what you don't want done to you.