I think this has been clearly explained. I'll just add that my nephew is a returned missionary and a recent Mason. He doesn't have a problem with the two coexisting. I was at one time interested in looking into Mason membership. I seem to remember that our church leadership said there was nothing wrong with becoming a Mason but their opinion was that one expectation of keeping things secret was enough.
Oh, and when you get as old as me, they are no longer considered horns, but two shofars.