PRACTICAL: For practical reasons, yes, yeast infection is an STD, because yeast infections can be passed sexually.
ACADEMIC: From academic perspective, NO, it's not classified as an STD.
WHO GETS INFECTED: People with AIDS are especially vulnerable to yeast infections, since they have a weaker immune system, therefore more prone to infections. However, it's not limited to people with AIDS. Yeast infection is common, especially for women. Women get it pretty often. And then, when a man has sex with a woman with a yeast infection, the man will also get the infection!