If, as you say, his parents are normally great, I would give them the benefit of the doubt.

Look, it isn't just whether work is okay with it. I've worked places like that, where dating was okay culturally and in policy terms. But it was just never really a good thing. It just makes everything harder than it needs to be. People fighting or breaking up at home leads to discord at work. People can't speak freely about their work frustrations with a colleague when their loved one is present. And so on. Professional people know this, they've seen it happen, and that's why they generally make it a rule of thumb not to get romantically involved at work even if it's tolerated by that particular employer. I would probably react negatively if my son did this in a high-potential work setting (although not in such an extreme way). It would signal to me that he didn't really understand what an important asset your job/career really is - that it's important enough to declare certain people off-limits romantically in order to preserve it.

Look, done is done and you're making it work. Good for you. It sounds like it might work out fine if you both have your heads on straight about it. But while I don't think your BF's parents reacted constructively, I think their concerns are very valid, and if BF acts like they're just being irrational or wrong for thinking that, they're just going to be even more convinced that he doesn't get it. I think your BF will probably have better luck hosing them off if he listens (when everyone is calmer) to why they're upset, admits that this probably was a complication he didn't really need to let himself in for, but explains that you're both committed to being absolutely irreproachable about how you manage this relationship in the workplace going forward.