You can remove git repositories at the command line.
git is something that is associated with a project. So you can create projects with or without git (or other version control). RStudio detects whether a project has git set up for it and provides some buttons to do simple things. You can also work with git at the command line - in the git pane choose More|Shell.
This is my go-to aid for RStudio git stuff:
http://r-pkgs.had.co.nz/git.html
If git is preventing you from opening a project, I would create a new project and copy the files across manually. The delete the offending old project.