Is this a rude thing to do?

Your son's being daft. That's what FB is all about. Posters want other people to read about their achievements or items of interest. If they didn't they would limit it to members only. As Deedaa says, it's not uncommon for strangers to message via FB because of a particular post. Maybe local history, a niche hobby or a recipe for example. In my experience it's usually warmly welcomed.

I don’t do FB but imagine what you were doing is fine. Isn’t this what FB is all about, sharing info and such like.

So many people do not keep their site secure..

That's a relief to know. He doesn't do social media.

I have contacted several people on Facebook because something in their profile has caught my interest. No one has ever objected to my interest.

Your son obviously doesn’t understand FB.

I thought the whole idea of having a profile was that others could look at it and see as much or as little as you choose for them to see?

What's the point otherwise of 'advertising' yourself if no-one is going to look at it?

The person who posted the photographs presumably did so in order for others to look at them?

I think your son is quite wrong to say you were being nosey.

No, I don't think so. Surely that's what the likes of Facebook is for? If people are concerned about their privacy, they can lock their profile down to limit who can view it.