Your parent's cousin is your first cousin once removed, but is it common to call them aunt/uncle instead?

Yes, in General American English, the descriptive label for the grandchildren of your great-grandparent that are not your parents or aunts/uncles (or children of one's cousin) is 'first cousin once removed'.

But how you address them is really not settled or commonly agreed upon in the US. It all depends on your family's patterns, how close you all are, etc.

Using 'uncle so-and-so' or 'aunt so-and-so' for such a person would be similar to calling any friend or person in one's parent's generation the same, that is, some people do it, some don't. Also, this kind of calling is probably only for children – as they get older, they'll probably call them by their first name. (Of course, the older generation will probably only use the younger person's first name in any case.)

So feel free to use it if all parties are comfortable with it, but I would say it is not terribly common but that could be because the incidence of knowing well one's first cousin once removed isn't that common.