Even if it would scare me (it really doesn't), as an EU citizen I would care about surveillance by the EU, not by the US.

> Imagine someone following you everywhere in the real world, even getting into your apartment and noting down everything you do.

To do what? Collect a lot of useless information? I would bother me if someone I know does it. I don't care if some abstract entity in a different country thousands of miles away does it.