Hero

Yes

If I had to say 1 or 0, I'd put her as a villain.

It depends if it benefits her

Anti hero

Mystique is considered a stain on earth.

... yes.

Seriously though I feel like she tends to swing between chaotic good and chaotic evil.

For much of her publication history, she's been pretty pro-mutant liberation, even if it means bombing civilians to do it... there was that period after Destiny died where she went off the rails... but love amirite.

However for her chronological history (as far as it's been developed), she's been kind of a self-serving snake.

... so I guess the best answer is villain?

Villain or Anti-Hero. Her intentions have virtually never been completely benevolent.

Yes

Villain outside most non source material, sometimes anti hero on source