I have had one diagonally symmetrical relay work in only one direction. I know it should have worked in both, but it didn't. Since then, if I am having a problem that could be a bad relay I always reverse it. It has been a waste of effort so far, but at least it serves to eliminate the question that I agree should not be there in the first place (but is anyway).Yes, the relays are diagonally symmetrical and can be plugged in either way without issue. It's true that some DC-energized relays have diode snubber and protections built in, such that the coil voltage must be applied in a certain way. But those types are not diagonally symmetrical.
In the same vein, I once had a battery explode when I was starting an engine and now I will never be in line of sight with any battery when starting any engine. 19 years and who knows how may engine starts later it hasn't happened again, but i still won't do it.