and these are questions you need to address with your doctor ... never be afraid to ask
As someone whose husband has had two allogeneic stem cell transplants I would automatically say no to community pools, a private pool that has been maintained with a limited number of swimmers might be OK. Public places might be OK, but wash hands and use sanitizer often, open doors/buttons with an elbow or knuckle as you are less likely to touch your eyes, mouth with those areas of your body. Most public places can be controlled, if someone is coughing or sniffling step away, opt for seats on the end of an aisle and when possible some distant behind you in case someone sneezes. There are simple precautionary measures that you can take to decrease the possibility of catching something without driving yourself crazy.
If one's immune system is compromised you should also be looking at a low microbial diet, no uncooked vegetables, fruits, rare or even medium cooked meats, no buffets etc. There are other items, we were told to not us a sponge after transplant (paper towels here we come) but you can soak the cleaning utensils in bleach, put them in the dishwasher or the microwave. Just be aware of what touches uncooked meats and vegetables and clean them often ... cutting boards, counters. Toothbrushes also carry quite a few germs so if your ANC (absolute neutrophil count) is low then change them often along with hand towels that are used by others.
All this being said, I do believe that when your immune system is severely compromised, when they intentionally try and wipe out your immune system in order to replace it with another immune system many threats come from within our own bodies from viruses that we all have and that surface when there is either no immune system or close to it play a large role ... CMV, EBV, BK, C Diff being a few.
Circling back, it depends on the severity so check with your doctor.