The Isar in Munich is safe and people swim in it all the time. It helps that it is not navigable, except by kayaks and rubber boats (sometimes).

The Danube running through Vienna is safe to swim in: https://www.wien.gv.at/forschung/laboratorien/umweltmedizin/... The water quality doesn't protect you from the current or the heavy boat traffic through. So most swimming is done in a disconnected side channel called "Alte Donau".

There's a nude beach there too (or at least there was 20 years ago)

I remember you can have a swim in Stockholm.

The rapids in the city center are famously clean enough för salmon and trout, but like any densely populated area there are also places and times of the year when the water isn’t good for swimming.