Clion (using CMake) gets confused when setting python interpreter

I'm using CLion (2020.2.5) with a mixed project: both C++ and python.

When I load the project from scratch, CLion picks up the CMake files and everything works fine on the C++ side. I get code insights, I can run unit tests etc.

Then I open a python file in my project. CLion suggests I set the python interpreter for the project which I do. Everything on the python side starts working (code insight, unit tests).

But when I do that the C++ side stops working, and I get that warning on every cpp/h file I open:

This file does not belong to any project target, code insight might not work properly

So far the only work around I found is to toggle the python interpreter (to No Interpreter) when I want to do C++.