If my girlfriend (fiance) wanted to go on The Real World I'd have to rethink being her boyfriend.

Maybe it's because I'm older, or because my best friend is female (and we don't have a sexual relationship), but I don't automatically assume anytime my girlfriend spends time with another guy there's a risk they'll somehow have sex. If they do, well, whoops, I'll have to find a new girlfriend. I'd rather find out ASAP that my girlfriend is prone to cheating then put a lot of effort into protecting myself from getting cheated on.

I mean, honestly, if your girlfriend is going to cheat, she's going to cheat. Preventing her from going to europe with her friend isn't going to stop it, it will merely delay it. Are you going to restrict her from seeing her male friend completely? What if they get lunch together and accidentally have sex at his place afterwards?

If you have issues with trusting your girlfriend don't be her boyfriend.