Irregardless isn’t a word; the word is regardless, which means despite or without regard.
I’m going out regardless of the bad weather means I’m going out despite the bad weather or even though the weather is bad.
The prefix –ir is a negative, so irregardless would mean not despite or not without regard. I’m going out irregardless of the bad weather means I’m going out not despite the bad weather or not even though the weather is bad, which makes no sense.
I’m going to quit my job irregardless of the consequences. This means I’m going to quit without not having any regard for the consequences or not despite the consequences. Again, this makes no sense.
What you want to say is I’m going to quit my job regardless of the consequences, which means I’m going to quit without any regard for the consequences or despite the consequences.
I see that irregardless is in more modern dictionaries as non-standard (it should be in there as substandard), and one on-line dictionary says that it is used in casual speech and writing and sometimes even by more educated people even though it’s considered to be a grammar faux-pas. That is a perfect example of what both Paul and I have said on many occasions: Just because it’s in the dictionary doesn’t mean that it’s correct, and just because someone who is considered to be intelligent uses it doesn’t mean that it’s correct. You have to look beyond that to decipher what’s really going on.
As I like to say, irregardless is not a word regardless of its presence in the dictionary.