Well, since no one replied I played around a bit more, broke the website and then started again and tried something new. This answer is really for peeps who come across the same problem and don’t know what the problem is or how to fix, so I hope this helps.
My problem was the .php structure of my permalinks. Our server is configured in a very stupid way (and unfortunately I can’t change it) so I’ve reverted back to the default permalink settings which doesn’t incorporate .php in the URLs. And now everything works fine.
So, if you have .php in your URL, bbpress user profiles won’t work.