No, “fuck” is a general exclamation. I can’t think of other examples, but it’s closer to yelling “oh my god” during a church service or something. Parkour is not a general exclamation people use. Fuck is. Like if something happens you might yell “fuck” even if it’s not sexual.
Another example is yelling “damn” at a “dam”, but that’s not really a good example because it’s more of a pun.
If you have one on one meetings it might be a good opportunity to ask (depending on the circumstances the other manager told you the feedback).
If you want to leave, then it’s enough reason to leave, but I would strongly recommend finding a new job before quitting.