Is it permissible to go to public beaches or swimming pools while wearing clothes that cover the the entire body, without paying attention to what others are wearing?

Going to beaches is forbidden because they involve the exposure of 'awrah (intimate parts) and reckless mixing between men and women, unless you intend to enjoin good and forbid evil. For whoever sees an evil and does not change it with his hand, or with his tongue, or with his heart, becomes a partner in sin. Allah Almighty says: (And He has already sent down to you in the Book that when you hear the verses of Allah disbelieved in and ridiculed, then do not sit with them until they engage in another conversation. Indeed, you would then be like them) (An-Nisa 4:140). One should be wary of Satan beautifying the idea of not caring about what others wear, as a gaze can be a path to temptation.