Paint white most definitely. Or you could faux paint them a light gray to look rustic, or just a simple gray .

Since the color doesn't coordinate well with the hardwood floors, I would definitely paint them white. They will still add some interest and texture to the ceiling without looking so busy or fake. Your other option is removing them entirely.

Friends of ours removed similar fake beams.

If you can’t remove them, paint them white.

If they are fake then just remove them completely. We did that years ago and it made the room look so much better!

Remove or paint the same color and sheen as the ceiling. They’ll practically disappear.

If we removed them we'd have to patch the ceiling a lot, so it's probably easier just to paint them.

Yeah I don't typically like fake ceiling beams, but I wouldn't find these all that offensive if they were white.

Just make sure you use the right kind of paint or hire someone to paint them who knows what they are doing. There are sadly even a lot of "pro" painters who will come over, give you a cheap bid, and then just spray a couple coats of latex over it and call it a day. They will need a sanding, a sealing vinyl or shellac primer, and then a trim enamel made for wood, which means NOT latex.

I will tell you that I think BM-Advance paint is overused on things it is not appropriate for like cabinets, but for trim the spray finish on that stuff will look like a million dollars on your beams.

I would remove them if possible they are so fake looking or just paint the same as the ceiling.

Since your wife likes them, I would leave them, but, I would most definitely paint them the white color of the trim. The color they are now, just does not go with your rooms.