Cesium and Strontium can be filtered out with ion exchange filters. You do have contaminated resin to deal with but that can be buried in an appropriate landfill. (That kind of technology is critical to light water reactors because they need super-clean water with carefully controlled chemistry to not have corrosion problems in the core and in the heat exchangers.)
The concern with that wastewater is Tritium which has a half life of 12 years
https://en.wikipedia.org/wiki/Tritium
Tritium is difficult to control for various reasons, one is that it is an isotope of hydrogen so it cannot be chemically separated from ordinary water. Those other isotopes you mention, particularly Strontium, are particularly dangerous because are bioconcentrated in the food chain
https://en.wikipedia.org/wiki/Biomagnification
but tritium doesn't do that. If it is released in the ocean it is going to mostly diffuse into a very big mass of water and literally be a drop in the ocean compared to natural radioactivity. It is not going to be concentrated in the bodies of sea plants and animals so it doesn't pose disproportionate danger to the fuel supply. The thing though is that radioactivity is super-easy to detect, there are roughly 6*10^23 atoms in 3 grams of tritium and just one of those atoms going "pop!" can be detected and many forms of decay have a unique signature so even amounts that are small compared to natural background can be detected for people to have concern about.