Should I accept doubled pawns to remove the opponent's bishop pair advantage? I understand that this can be very situational which is why I don't provide a position as I am seeking some more generally applicable answer or things to consider.

Assuming that the opponent has a bishop pair would you feel that a combination that leaves me with doubled pawns and the opponent with only one bishop (but no other difference in material). is worth it? I guess another way to ask the same question is whether doubled pawns are a half point disadvantage.
In general, the two bishop advantage is worth half a pawn, while double pawns are only a minor disadvantage. Sometimes doubled pawns can be an advantage if they do not block your pieces and control important squares. OTOH, creating doubled isolated pawns on a half open file is likely to be worth the loss of a two bishop advantage.

Long term imbalances that occur early in a game are easier to deal with than those that occur late in a game. Let us take for instance the Nimzo-Indian line



[FEN ""]

1.d4 Nf6 2.c4 e6 3.Nc3 Bb4 4.a3 Bxc3 5.bxc3 c5 6.e3 O-O 7.Bd3 d5 8.cxd5 exd5



Black has just allowed white to undouble the pawns that he gave up his dark square bishop to double. The key to understanding this is that the doubled pawns are not such a big deal. Black is looking to keep white's dark square bishop permanently bad (because of the pawns on e3 and d4), while getting good squares for his knights. Black's light square bishop will be not so bad (still bad because of the d5-pawn) and will also look for opportunities to trade his light square bishop for white's.