Allergies are always, always, always a reaction to protein. You can develop an allergic reaction to probably any kind of protein, but some are fairly common. An actual allergy doc could probably explain why.
Celiac is an auto-immune response caused by a genetic defect. It is not, technically, an allergy. If you do not carry the celiac gene defect, you can never develop celiac disease.
There are other kinds of wheat and other grain sensitivities, but "associated with" is a sciency sounding way of saying that people who complain of A sometimes complain of B.
Allergies are acquired - typically due to exposure of one sort or another. Celiac is a gene that a small number of people have, which is a matter of breeding and luck, and whether that gene is expressed is a matter of luck. Once expressed, there is no evidence that it ever goes away, and unlike allergies there is no exposure treatment that can reduce the sensitivity.
Yeast is a fungus but not closely related to edible mushrooms.