Is there a linguistic term for this?

E.g. You can take a girl out of a city but you can’t take the city out of the girl

“I don’t think that evolution is supremely important because it is my specialty; it is my specialty because I think evolution is supremely important”

Possibly an antimetabole:

I call it the “Camisado Effect”.

It’s called Chiasmus.

Or, one of my personal faves:

If you fail to plan, you plan to fail.

ianzin, according to the Wikipedia entry for chiasmus, although some people refer to structures like the one in the OP as chiasmus, other people think that it’s more correct to refer to them as antimetabole:

In Soviet Russia, Camisado effects YOU.

Isn’t antimetabole really just a subset of chiasmus, though?

It depends on how you define the terms. Read the two entries from Wikipedia that I quoted. Some people define “chiasmus” specifically to exclude antimetaboles, some people define it to include them. Do we really want to get into an argument about which definition is correct? Unless you have information that Wikipedia is clearly wrong, I have nothing more to say.

Good call, Wendell. I know more than I did before!

“Antimetabole” is a pretty nifty word, at any rate. Trips off the tongue better than “chiasmus”, which sounds rather too much like a gynaecological complaint.