Two alliterative sentences railing against this:
Irrespective of the irresponsible initiative of those at institutions that produce dictionaries that resulted in the term "irregardless" being integrated in to its pantheon of inclusion (with the implicit acceptance), if the definition of said term is a mere variation on "regardless" then such indiscretion disintegrates any importance of even any modicum of codification to our language (that presumably we were to infer from their effort to generate the list of the lexicon), rendering the integrity of investigating words in a dictionary to the point of irrelevance.
To adopt a misused word merely because it received an implausibly high level of utterance in common parlance seems highly irregular intuition on the part of those who ajudicate what gets imported—especially in light of the fact that there's already a perfectly good word available that holds the intended meaning by those using the longer (and more multi-syllabic) variation—makes the decision essentially irreconcilable, even if duly indicated as improper.
Three less-alliterative paragraphs that offer a compromise (of sorts):
If in all other application of the prefix "ir-" to a word changes the meaning of the new word to be opposite of the original, the conventional meaning of "irregardless" would be the opposite of "regardless" (in the same way that, for example, "irresponsible" means "not responsible"). That, of course, is not the case.
"Regardless" itself is already essentially the opposite of "regard," with the application of the "-less" suffix ("without regard to"), so ultimately that should make "irregardless" mean the same as "regard" but holding the implication of meaning "not without regard to," for contexts where one wished to refute where another had failed to regard something one thought worthy of that.
With that definition there'd be no irredeemable redundancy to what has been introduced, something filling a need rather than being merely what someone who didn't think through what he meant to say, followed by another who didn't think through what he meant to say, followed by another who didn't think through what she meant to say….
A conclusion about which all might be able to agree, but probably not:
Let's dispense with such topics, as concern for English making sense surely must be deemed irrational and itself can even be considered indefensible.
When it comes down to it: Who bothers with dictionaries any more except when playing Scrabble? Thus, all this energy suffices in arbiting board games.
(Let's not go down the path of pondering who still plays Scrabble.)
Interrogatories? Irascible diatribes?