I sided with the Railroad during the main quest, which meant I had to destroy the Institute. Now when I talk to Preston Garvey he always says the same thing, where he accuses me of killing innocent people needlessly, and he won't follow me anymore. Is he supposed to do this? As I understand it, siding with the minutemen also results in the destruction of the Institute.

I can't really tell if it is intentional or a bug, since he never outright says "I'm not going to follow you anymore"--he is just stuck in a dialog loop. He also will still give me minutemen quests, but if I talk to him again after receiving a quest from him he'll just repeat the same disapproving dialog about the Institute's destruction.

Anyone else who sided with the Railroad encounter the same problem?

I'm guessing you didn't sound the evacuation on Father's terminal? Preston won't like that.

He is fine if you set off the evac signal.