What It Should Mean
"Regardless" is most often used in modern conversation to cede a minor point while simultaneously dismissing it. As in, "It's true, Gary, you could probably take the Funland security guards. But regardless, you're still using company property to defraud a nickel arcade."
"No, Gary, I don't think Billy is 'rubbing it in your face' -- I think he just really wants that skull ring."
Let's let "irregardless" officially take over that one specific use of "regardless."
Irregardless: When you do actually have regard for the subject matter but you just don't want to talk about it with that person anymore.
"Yes, I do admire the works of Godwin, Gary. But irregardless of anarchic philosophy, let's at least put on some pants, OK?"