Well F# from the very beginning has always had a bit of a rebellious nature seeing as it was brining ML style programming to the traditional OO platform of Microsoft's .NET. Because of that, many F# people do not use Windows and F# is very much built to be as independent from Microsoft as possible. See here for various ways to use it on linux:
It's not dependent on Visual Studio at all. It has its own build chain (FAKE), runs under Mono and ships independently from .NET. It's the most open-source of the MS projects.
Core language works fine and no dependence on VS. There are packages for most distros. Libraries outside the core language are a bit hit and miss, but you'll find libraries for most things you want to do.
If you have a Windows project where you've been NuGetting stuff from all over the place, porting might be a bit of a pain.