“She’s got a ticket to ride, but she don’t care” — why? [duplicate]

The intentional misuse of don't is a form of code switching (or code mixing). The form is extremely characteristic of working-class southeastern Americans ("southerners"), who are also the primary audience for American country music.

What is most interesting about the song is that Shania Twain is Canadian — and that is where the code switching begins. It is a deliberate error made in attempt to establish authenticity and to better connect with her music's intended audience.

The use of don't instead of doesn't is an error in standard English, of the sort you were probably taught. However, this sort of error is characteristic of many non-standard, rustic dialects, and country music of the sort that Shania Twain sings is known for using these dialectical features as part of the conceit of being rural, Western [1], and unpretentious.

[1] As in the American West, i.e. cowboys and Indians.

It's because the song is in non-standard English and don't is used for doesn't in some non-standard varieties of the language. It's important to understand that 'non-standard' doesn't mean 'sub-standard'. It don’t matter is ungrammatical in Standard English, but not in other dialects, such as those in which popular songs might be written.

Some varieties of English use do (and negative don’t) for all persons and numbers as the auxiliary form in the present tense. As Peter Trudgill has pointed out:

Standard English fails to distinguish between the forms of the auxiliary forms of the verb do and its main verb forms. This is true both of present tense forms, where many other dialects distinguish between auxiliary I do, he do and main verb I does, he does or similar, and the past tense, where most other dialects distinguish between auxiliary did and main verb done, as in You done it, did you?