In short, possibly. You can’t delete or reorder values which can be mildly to very annoying, or not annoying at all if you don’t run into it 
While I do agree with @champeric that pg enums are nice and I have used to use them, my counter experience is that I’ve never run into any of the caveats of using plain strings. If storage isn’t an issue, I find them much more convenient. While I’m big into fkeys and partial indices, tracking down rows with a mistyped status is orders of magnitude simpler than dealing with orphaned rows. That’s just an example, though, I’ve never actually dealt with the former.
