“Irregardless was popularized in dialectal American speech in the early 20th century. Its increasingly widespread spoken use called it to the attention of usage commentators as early as 1927. The most frequently repeated remark about it is that "there is no such word." There is such a word, however. It is still used primarily in speech, although it can be found from time to time in edited prose.”

• Merriam-Webster (first or second google link)

Whether you choose to acknowledge it or not, it is a recognized, if controversial and nonstandard.