I am allergic to dust and a good many other things too. Should be in my own bubble, but it wouldn't be much more tenable than what I must go through now.
It is in fact the dust mites that are the problem for most people allergic to dust. Just as it is the waste that is produced by bacteria that cause trouble on your teeth in the form of plaque, so it is the waste produced by dust mites that cause the allergic reaction for most people, myself being one.
Why would you think a person couldn't be allergic to dust? Aside from the dust mites, do you know what makes up dust? Pollen, dead skin cells, and anything that can be dehydrated into dust.
From Wikipedia: Dust in homes, offices, and other human environments contains small amounts of plant pollen, human and animal hairs, textile fibers, paper fibers, minerals from outdoor soil, human skin cells, burnt meteorite particles, and many other materials which may be found in the local environment.
So you see a person could be allergic to any one of the above ingredients or all of them. I am deathly allergic to animals, including some insects, so it reasons that certain products of those same insects if found in the dust would cause a reaction also.
I'm often allergic to my own daughter because she is sometimes covered in cat or dog hair/dander, etc. Anything with the offending material on it will cause a bad, sometimes very serious reaction in me.