I understand that you never met them, and indeed, I agree with your, and others, point there.

I have never contacted my best friend's girlfriend. The other way around, I never really had a girlfriend so I never had to think about their friends.
I doubt I would really do it? I might consider it is I am concerned that I am not connecting with her friends? I doubt it. In my mind, how would my GF think more highly of me when I connect her friends? No, I can never see myself do that. I can see myself thinking I need to become friends with their friends, at least a little bit. I mean, it is how two couples develop this kind of couple friendship. But then both need to be taken. Otherwise, you have this strange triangle, and you are the third wheel. Which would make it odd.

Surely, most men would want to be on good terms with their wife or girlfriend's female friends. I think most men think, wrongly or rightly, that this is an important criteria to meet. That her girlfriends approve of you.

But surely, the female partner here is the one who ought to control all this. If she knows nothing about this (and I think here we don't know for sure but we can assume she probably doesn't), then that is indeed kind of controlling.

Why wouldn't it be caused by insecurity? Or just something with no thought behind it (in the second Facebook case?). I mean, this whole idea that they saw your picture and that they now lost their minds, really?

I think I would bring it up, casually. Not expressing all your concerns. See how they respond to it. If this would worry them, they would want to know. And you wouldn't want to keep a secret from them. Even though you just reconnected. I guess it can be kind of tricky if they have been together for years, and now you come along and cause a problem in their relationship, if that is really what it is.