You are right that FP and OO are not opposed BUT they are very different mind sets.

While F# might run on an OO platform it is still a full FP language based on ML/OCAML (It is missing higher kinded types but that was the .NET platform that caused that limitation). MS just bolted on syntax that allows it to interact with C# and the other languages hosted on .NET

Trying to do OO in F# actually causes a lot of limitations in the language. Things as basic as the pipeline operator failing to play nice once you start using "member" variables. Things just do not compose as well :(

Functional programming is really a complete mental shift from OO. No classes, just data and functions. Oh and functions are also data.

I have written a series called Functional programming for the OO developer, currently intro and 4 parts that explores the difference in mindset of the two style for OO people.