You can use dotnet new -i MonoGame.Templates.CSharp to install dotnet templates which should work out of the box without having to install anything else. Obviously you will need to generate templates from the terminal, but I don’t think that’s an issue for an average Linux user (ie. dotnet new mgdesktopgl will generate a MonoGame DesktopGL template).
As for the shader issue, technically you can compile them with Wine, I could make a tutorial on it, and probably integrate it into MonoGame by default. I’m always hesitant to do that as its not native…