And yet one of the father's of written modern English, Chaucer himself often used double negatives [0].
ex:
"Ther nas no man no wher so vertuous" ("There never was no man nowhere so virtuous")
"He nevere yet no vileynye ne sayde / In all his lyf unto no maner wight" ("He never yet no vileness didn't say / In all his life to no manner of man").
The modern English language (written and spoken) has been in constant flux for the last 600+ years. What was once required is now antiquated, and what was once verboten is now required.
At this moment in time, double negatives are frowned upon. However, that may change in the future, and it's possible that irregardless is the start of a new set of changes in the language.