Heck, even the Wikipedia article on going to makes a note of it:
It’s interesting, because the ‘to’ is different in each case as well. You can’t use gonna when ‘to’ is acting as a preposition. Is it maybe because the contraction would cross a phrase boundary?
Fowler says ‘to’ used with an infinitive is a particle. Maybe when it attaches to the main verb, it is kind of like a clitic. But at other times it belongs with the infinitive (e.g. to be or not to be) so it seems ‘wrong’ to attach it to elsewhere. (not saying it is wrong, that just it sees that way to some people).
Calling it vulgar isn’t offensive if you use the proper definition of vulgar
Vulgar just means what is common speech, different to formal writing
Are you referencing my earlier post? If so, then, yeah, I know. It was just an attempt (probably disastrous) at what you Earthlings call “humor”.
Common, colloquial, informal, formal–these are called “registers” in Linguistics (Socio-linguistics).
It’s what teachers try to get students to grasp today: You can use your own dialect in informal situations, but there are registers in which you need a command of Standard (formal) English.
Compare “don’t”, a common abbreviation of “do not”.
It’s acceptable in speech in all almost all registers, except the most formal. We wouldn’t be surprised to hear it used in a presidential inauguration address, for instance. But I don’t think we’d expect to hear it in, say, the language of a wedding service.
In writing, its use is a bit more restricted. It’s never wrong, but it’s avoided in the more formal registers. You won’t find it in legislation, or in academic writing for publishing, say.
It’s sufficiently well-established as a written term to have a ‘correct’ spelling - “don’t”. Anyone writing “dont” will be corrected.
“Gonna” isn’t quite as well-entrenched, but it’s moving in that direction, at least in American English.
Is it signficant that this happens particularly with auxiliary verbs - don’t, won’t, gonna, hafta? The literal sense of those verbs is unimportant when the function as auxiliaries, so preserving the pronunciation/spelling becomes less important. Or something like that.
There was a recent discussion of this in one of the all-too-common, “People are butchering the English language!” threads. Ellie303 said that, “it can make people sound uneducated,” and I pointed out that all you have to do is listen and you’ll hear that everyone says it, including the most educated people in the country..
People who claim that they don’t use gonna are just ignorant of their own speech.
To answer the OP, its “linguistic status” is that it’s a reduced form (or relaxed pronunciation)–and it has been for a long time.
It’s kinda ambiguous. 
Americans need not fear that Brits will be offended by this word. Most Brits use it. In my neck of the woods (Gloucestershire - the UK equivalent of a West Virginian redneck community) we don’t even pronounce it the same way depending on where it appears in a sentence or what it means. For motions, its sounds like GOH-NOO. If it appears at the end of a sentence it sounds very much like GUN-NOO.
And most of us don’t really even say “going to” when we are speaking spacially. We say “goin’ to”. Make fun of Palin all you want for this speech habit, but Obama is just as “bad” when it comes the gerund of most verbs. Being from New England, myself, this is very natural and very much a part of the speech you hear there-- a bit more exaggerated than you would hear in some other parts of the US.
That’s why, in some regions, people say “fixin’ to.”
To give an example of what you wrote: People say “I’m going to the store.” You can’t substitute gonna there. “I’m gonna the store.” is not heard. The natural casual speech would be “I’m gonna go to the store.” The use of the preposition is so instinctive that it appears whenever necessary as a part of grammar.
For me, an amateur linguist at best, this indicates the power of native grammar - the base rules that govern how native speakers put words together into sentences. (Also basic Chomsky and why he was so influential for so long.) It also indicates that colloquial, informal, or casual speech should not necessarily be considered mere ignorance or perversion of formal language. Elision, compression, and slurring are natural parts of spoken language and there is evidence of it all over English. Double negatives are not mistakes but one form of emphasis, which is ubiquitous, as is very unique or other modifiers of formally singular terms. It’s the written language where true errors are more likely to proliferate. I’m against the use of apostrophe’s in plural’s as much as anybody. But nobody says the words that way.