Irrespective is almost as in disrespectful, but not entirely.
It's less of a disrespect and more of an ignorance or disregard. In
a sentence you would say, "Joe took his new Mustang and totally
tore up the road, irrespective of the law and peace for the
locals", or "Smokers are so irrespective of non smokers" in the
sense that smokers would show no regard for people who do not
smoke.