spect: derived from Latin "specere", meaning "look"
-ive: of doing something
So irrespective means:
Of no need to look at something again and again.
If something is "of no need to look again and again", it must be not important or not relevant.
Evolution of usage
Everyone should be equal in law, no need to look at the social position again and again.
Everyone should be equal in law, irrespective of the social position.