If you feel the need to ask, then stay out of the pool.
Exactly. Folks should think it through. If people who appear to be grungy use the pool, they aren't likely to be hygienic when they're in the pool. A shower wouldn't change that. The question NEVER should've been directed to someone using the pool. The issue is with whomever is supervising the pool.
I don't trust at all anymore that public pools, even on cruise ships and mid-range hotels, are clean. For that reason, when I swim, it's when the pool first opens in the AM.