"It doesn't matter" or "It don't matter"

In the 16-ish century both of "does not" and "do not" were shortened to "don't". "Doesn't" appeared a lil bit later though... However it is still used in some rural dialects. It is okay to say "it don't matter" instead of "it doesn't matter" if it is kind of informal speech

"It doesn't matter!" is correct, but usually the americans could say "It don't matter!" It's a way to say informally.

"Does" is for a singular noun (but only in the third person as pointed out by snailplane), and "do" is for a plural noun. You could say "they do matter", but "it does matter". Adding the word "not" does not change the rule:

It doesn't matter.

Never expect that song lyrics or similar texts (such as stories) will use "standard grammar." Lyrics and other such texts employ the grammar of the person who wrote them ... even if the author uses grammar that differs from standard grammar.