The word appears in dictionaries, which document usage, but the word is nonsensical. "Irregardless" is used to mean "regardless", which is a far better choice of word.

  irregardless (adj.)
  an erroneous word that, etymologically, means the opposite of what it is
  used to express; probably a blend of irrespective and regardless, and
  perhaps inspired by the colloquial use of the double negative as an
  emphatic. [1]

[1] https://www.etymonline.com/word/irregardless

English would be a lot more compact if we removed all the nonsensical and previously-nonsensical words.

Start with the auto-antonyms: https://en.wikipedia.org/wiki/Auto-antonym

* Cleave can mean "to cling" or "to split apart".

* Clip can mean "attach" or "cut off".

* Dust can mean "to remove dust” (cleaning a house) or "to add dust" (e.g. to dust a cake with powdered sugar).

* Fast can mean "without moving; fixed in place", (holding fast, also as in "steadfast"), or "moving quickly".

* Ravel can mean "to separate" (e.g. threads in cloth) or "entangle".[11] Sanction can mean "approve" or "penalize".

* Table can mean "to discuss a topic at a meeting" (British English) or "to postpone discussion of a topic" (American English).

Similar to bone and debone, ravel and unravel, and countless others I'm sure.

Stan Kelly-Bootle used to call these self-antonyms.

Literally!

It's a perfectly cromulent word.

Unlike “inflammable” which is virtually guaranteed to confuse.

"Inflammable means flammable? What a country!" - Dr Nick Riviera