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You certainly have to be real careful, there are some ferals out there who treat the public toilets as though they were at home and fail to wash their hands after using them, you only have to hang around the pool deck for a few hours to see it.
I flat out refuse to use any toilet other than that in my cabin, its not fool proof, but definately reduces the risks.

Same with the pool, i wont set foot in the main pool, you'll find me down back in the adults area.
The first two cruises i went on kids spewed and crapped all through the main pool so it was closed for 24hrs whilst it had to be drained and cleaned.

When i go for food or a drink, first thing i do is look for the handwash.

Whilst we've been fortunate enough not to suffer a Nurovirus outbreak on the cruises we've been on, the risk is always there so its best to do whatever you can to limit your chance of exposure.