Is irregardless a word?

Yes, technically, and the dictionary defenders are correct on the narrow point: irregardless appears in Merriam-Webster and has for many decades, because it meets the criteria of a word, sustained, widespread, meaningful use, documented back to the early 1900s. Dictionaries describe the language people actually use; they do not issue licenses.

But read the entry: it is labeled nonstandard, and Merriam-Webster's own guidance is to use regardless instead. The objection is fair, too. The ir- prefix and -less suffix are both negations, so the construction argues against itself, probably born from regardless colliding with irrespective.

So the complete answer is: a word, yes; a good word, no. In any context where your credibility is on the table, a resume, a memo, an argument you intend to win, irregardless functions as a small self-inflicted wound, because a meaningful share of readers will stop evaluating your point and start evaluating you.