Not showering before swimming

Hmmm - really winds me up this but am I being too fussy ?
I can’t stand seeing people getting into my local swimming pool without showering first - really makes me feel a bit queasy. Likewise, at the gym, people getting into jacuzzi without showering.. .
Am I being overly fussy ? Does the chlorine negate the need to shower ? If someone has a dirty arse it’s only going one way . . Just icks me out . .
Overly fussy or should I be stopping people from getting in the pool ??? ( sure that would be appreciated…)
Comments please

So I guess I’ll have to start saving up for my own swimming pool . .