Do factions and companions care what other factions you associate with?

As far as joining goes, you can join all of them without any problem, at least at first. I'm a member of all factions and no companion complained so far.

I even took Nick Valentine with me when visiting the Brotherhood, which results in a few comments but nothing more.

At some point there are consequences for doing certain missions with a faction, but I stopped before the point where I have to decide and avoided it so far. So I can't tell anything more about the late game. But you can certainly join all the factions at first without worrying about your companions.