Is “she don't” sometimes considered correct form?

You should understand that, in school, you will be taught a certain kind of "formal" (or "standard") English, much the same as what native English speakers are taught. This is not necessarily the same English that many people actually speak. A regional or cultural style of language that is different from the "standard" is called a vernacular.

Vernacular isn't wrong or bad English. It's just different English, although it may be associated with a particular social class or culture or even ethnicity, and it may not be appropriate to use in every situation.

"She don't" is one such example. To some people, this is perfectly normal English, and clearly it's OK to use it in music or poetry. But because it's not "correct" grammar, people who use it might be considered lower-class or uneducated. It's usually not OK to use it on a school paper, or in business, and definitely not OK to use it if you aren't familiar enough with the vernacular to make it sound natural.

Remember, there is a fine line between imitation and mockery.

Personally, I would never say "she don't" -- unless I was trying to imitate that vernacular. Which I do, from time to time.

3d-person singular don't is quite common and unremarkable in speech communities where formal correctness is not held in particular esteem. It should not disturb you.

But it's not acceptable in communities where formal correctness is valued; and since doesn't will not mark you as a pedant or an outsider in any speech community, there is no reason why you should make any effort at all to emulate the informal use.

Your question is clear and concise, and warrants a clear and concise answer, without equivocation:

Is “she don't” sometimes considered correct form?

The answer to that question is:

No.

The construction she don't is never considered to be "correct form."

It may be acceptable, or part of a vernacular, or idiomatic in some communities (and employed both by those in whose dialect it is a natural utterance and by songwriters who pretend to be conversant with such dialects for financial reasons) but your question does not introduce any of these qualifications. You ask whether "she don't" is sometimes considered correct form.

The verb do is an irregular verb. While there are a multitude of idiomatic or vernacular conjugations of this (and of many other) English verbs, there is only one correct conjugation of do in the present tense, and it is:

I do
you (singular) do
he/she/it does
we do
you do
they do

Thus, the only correct negative form in the present tense with the feminine third person singular pronoun is:

She does not (doesn't)

What the other respondents fail to mention is that there is a whole dialect in American English (i.e., black inner-city English), that uses "don't" in the third person singular as a matter of course.

Although you can hear that, and things like it, in practically every rap or hip-hop track put down recently, and nearly every rock song since the '50s—including the one you cite—its pedigree goes back well before that. Here's a song from 1931 by Duke Ellington ("It don't mean a thing if it ain't got that swing") that perfectly illustrates the license that black English takes. And note that it has every right to do so.

There's more to English than sounding educated.

"She don't" would be vernacular and I think any English speaker understands it fine and many English speakers prefer to speak that way. However, it is not business English, and if you are a language learner I would not use it. I would not say it is "correct", i.e. it would be a mistake in any written English exam or paper.

The best way to understand how it is used is to listen to people who use it. Song lyrics are a start (but note there's a chance the songwriter just wants "don't" to fit the meter, and "doesn't" does not).

"She don't" is incorrect english grammar. It's true, as many have pointed out, that it's in use in many different contexts where correct grammar is unimportant. But the OP is trying to understand the language, not make value judgements. As a learner of Italian, I don't want to know about the dialects spoken by 70% of the population. I have enough trouble learning the primary language. But I do want to know when I hear things that sound wrong that they might be due to dialect influences. And I need to understand the difference.