Well, you certainly wouldn't be the first to believe that! One person thought they were a gay couple serving some sort of "Scarlet Letter" type sentence. The most common belief, though, is "cult". They've also been accused of being door to door salesmen, devil worshippers, and government agents... Really, most of them are sci-fi and cult classic nerds with hidden athletic or artistic talents...Healing vibes for your foot, that sucks
We have Mormon missionaries over here in Europe, too. At least I've seen them in bigger towns sometimes. Always young men with black slacks, white dress shirts, backpacks and a nametag, always in pairs. They're very polite and friendly, but for a long time I always thought they were super shady, con-artists probably, until someone told me what was up with them. I have no idea what they're doing in Europe, but I've never seen them talk to anyone of their own accord.
Mormons serve missions in any country where religious freedom permits them to be. They're in Europe because they were called to serve there when they applied for their missions. Serving a mission anywhere is hard, though, as they face frequent (and often rude) rejections on a daily basis (imagine telemarketing)... You will find that there are a LOT of LDS Christians all over Europe. For an idea of just how many, you can GoogleMaps LDS temples... The Church only builds temples in areas where there are enough members in a given area.Interesting. I imagined them to be very... tame? Conservative? Traditional?
But really, do you have an idea what exactly they're doing in Europe? My partner once told me that Mitt Romney was in Europe once as a missionary for the Mormons and started hating Europe so much because he wasn't treated very well. He has no idea if there's truth to this story, though, but I found it interesting, especially because he said he had heard that many young Mormons returning from Europe had made similar experiences. Makes me wonder even more what they're doing over here.