Nope, definitely not normal. I like a nosey as much as the next person, but I'd never, EVER, wander around someone's house without their say so, and wouldn't ask to be shown round either. It's someone else's home, not a tourist attraction!
Friends often ask if I want to see their house if they've either recently moved, decorated or had some work done, but if I've seen their bedroom once when they first moved in, I have no desire or need to nose around it again.
Similarly, people always ask if it's OK to use our upstairs loo, rather than downstairs (if we've got people round there's occasionally a queue!). The point is, they always ask, and they don't wander around while they're up there.
I've used the upstairs loo in my SIL's house in the same circumstances and I'd never go wandering in to their rooms! My DN wanted to show me his bedroom the other week and while I went with it, I asked his DM first and still felt awkward about it!
The fact that you have multiple of these types of friends OP is rather bizarre to me!
But @MrsAriadneOliver OMG I'm so jealous. I'd have loved that as a kid - I used to fantasise about hidden doors and corridors in stately homes as a child. What a wonderful time you must have had!