The advantages and properties exhibited by XOR are also exhibited by XNOR, like the ones mentioned in many answers like this one
Information is preserved. $c = a \oplus b$. One may recover $a = c \oplus b$ (and $b = a \oplus c$).
Information is hidden. One cannot know anything about the inputs from the outputs.
I found this answer which talks about the efficient implementations present in the instruction sets, and programming language, but this sounds like a "who came first, chicken or the egg" problem.
Is it that the efficient implementations exist because XOR was chosen over XNOR?
There are mentions of some architectures which have XNOR support.