Can a highly experimental paper with potentially controversial concepts published on a preprint server (not in a journal) damage one's career?
Imagine a paper which has unconventional ideas which could be controversial. Does publishing it on a preprint server have the same negative career implications as publishing in a journal?

Yes, potentially. You are making your thoughts and beliefs about a certain subject known publicly. Depending on what those thoughts and beliefs are, this can damage one’s career even if done in a tweet, email, stack exchange post (hmm...) or any other medium of expression. A preprint server is no different.

Or is a preprint server actually an appropriate place to get feedback on this type of paper?

A preprint server is an appropriate place to get feedback on scientific work that’s maybe incomplete but is very close to being complete. Nonetheless, the potential for career damage if the work is of very low quality or reveals you to be a delusional or incompetent person still exists. If that is a concern, consider looking for feedback in more discreet ways.