It's annoying that in 12 years they never answered the question of whether May is a mutant. She probably fits the literal definition of "mutant" (although even then I could think of non-mutant explanations for her powers), but being a mutant, in the Fantastic Racism Marvel Universe sense, doesn't mean "has a mutation". It means having an X gene and being subject to mutant detectors. It also means "treated like a minority", and not knowing whether she's one is like not knowing what ethnic group you are, in a culture where passing as white is a very real issue.
This is particularly annoying because the mutant issue has been brought up—but even then May never asks whether she herself is one. Not to mention that her dad is a scientific expert and can contact more experts, all of whom can easily find out.
I think May answered this herself, albeit in a somewhat unrelated event. When there's a bit of a Mutant Scare at her school, May sympathizes with the mutant in question, and one of her friends asks something like, "What, are you a mutant too?" May responds with something along the lines of, "And what if I was? It's good to know that you'd feel differently about me if I was."
That said, she probably isn't. She seems to have inherited her powers directly from Peter, who isn't a mutant.
She definitely doesn't have the X gene because she was never approached by the X-People.
I understand why May can't reveal she is Spider-Girl, but why can't she reveal that she has some limited subset of powers? Just saying "I am a mutant with super-strength" (assuming she is a mutant) would be enough to explain why she can't play on a sports team and would let her openly sympathize with other people in similar positions.
Part of having a working secret identity is making sure people don't have reason to suspect there's something different about you in the super-powers department. Her admitting to super-strength doesn't preclude the possibility of the other associated powers, and would change the speculation from, "'Hey, May never seems to be around when Spider-Girl is...' 'Nah, I don't think she's the type.'" to "'Hey, May never seems to be around when Spider-Girl is...' 'You know, she did say she has super strength. Isn't that one of her powers?'"
Meagyn Brady — is her invisibility symbolic, or is she really a mutant/super with the ability to fade into the background and avoid detection if physical contact isn't made?
Given that she's completely unnoticable to most people even if interacting with them (like her mother), perceived normally by others (like Mayday), and seen by some only if someone else draws their attention to her (like Courtney), and it first manifested at a clearly defined moment (her father's funeral), the most likely verdict is that she is indeed a mutant with an ability to selectively become unnoticable which she cannot control. She is not litteraly invisible, but she may as well be.