The "conditional if" plays a role of a subordinating conjunction.
While I haven't found a source to say so, I gather that this may be freely paired with "then" in the standard "if-then" clause. The correct comma punctuation would seem to be:
If it's a square, (then) it's a rectangle.
(Then) it's a square if it's a rectangle.
(I think use of "then" in front is uncommon, but I don't know if it's ungrammatical per se.)
I found a few places on the internet where "if-then" was categorized as a correlator, but I am inclined to disagree. There is no parallel structure, and the punctuation does not match up.
I am guessing that "if-then" is sometimes mislabeled as a correlator when some people ineptly conclude that "correlative conjunction means a pair of conjunctions".
Can anyone review these thoughts and offer any details I overlooked?