What common diseases might be difficult to fight if you have weakened immune system/cancer?

I'm one of those people. I can tell you that almost anything is a threat.
Colds
Pneumonia
flus (it is recommended that we get flu shots but I have an egg alergy and try and get arond that).
Some people have trouble with cuts or severe nose bleeds. I'm not one of those.
measles mumps almost anything that can be fought with white cells. The

Problem is that anti cancer drugs affect your immune system which happens by lowering the white cell count. For me that is the worst possible news. My cancer does that all by itself.

Fevers are not very helpful. Doctors really get nervous when someone on chemo gets a fever, especially if they have neutopenia (low neutrophils). They give you the strongest antibiotics in their cupboard.

Tooth aches. They're afraid you might start to bleed. If you have low platelets (again from Chemo or naturally going lower) then bad bleeding will be a problem.

Well I've got you started. Just google low white cell count. You should be able to find things that I never thought of.