Where are these doors going into ? As for color IMO those doors you show are pretty heaviy looking for that space IMO I would look at something much less rustic for sure.

Is the dining room the larger space we're looking into from what appears to be the living room? If so, do you really need barn doors (or any doors) there? Barn doors are going to be a very prominent feature, and I'd worry they might overpower the space and limit decorating options. If that is the dining room, consider too how close barn doors will be to the slider. Isn't that going to be really busy? I just think you have such a nice open feeling in this space right now, and I would be very hesitant to close that in with bulky-looking doors. There are so many other options for achieving a farmhouse vibe.

That said, if you're determined to have barn doors, I would agree with your boyfriend and go with the lesser obtrusive white.

It's not so much the color of the barn door as the hardware you choose.

Not sure I'd be deciding on anything until the room is painted TBH.

The doors would be going onto the larger opening (the one on the right).

Barn doors are finished carpentry- wait until your floors are in.

I have barn doors that cover an area twice that size. They are a statement to say the least. They match our floors.

another idea would be glass barn doors. These are stunning.