I don't see any problems with .git. Most go packages use git anyway, it would be pretty amazing if go tooling would break if you have a .git directory anywhere.
Re the other question: If you don't run a go command with a path name, it doesn't matter what the directory structure is. I have tons of non-go projects in my GOPATH and build them with the usual tools. No issues.
I also set GOPATH=$HOME, and all my source code (not only Go) lives in $HOME/src, and I do use git for both Go and non-Go projects (so they have a .git directory in $HOME/src/what/ever/.git), and there's no problem. Why would there be one?