I started using public showers and bathrooms in 1978 when I joined the YMCA and went everyday before work. I continued that when RVing.I guess that makes it about 35 years now.
I have never had a health problem with them. We have always used our shower in the RV for storage and hanging clothes. Some of us don't have the money to buy large RVs as the OP must have.
Most of us do not care where others shower. I also don't care to know why so many RVers eat out all the time instead of using their kitchen. Nor why RVers buy desert when they can make it themselves. In fact I never ask those questions.