It is really difficult to help you with only those info. It could depend on your code, on you computer, on your OS, on many things.
The only reason I see for git to act when your project is running is if you are generating lots of file that are not in gitignore so not untracked. Git would see those, and IDE would try to update the git pane. It is a wild guess.
R process should not be impacted by git process anyhow. Unless you are short on memory or low performance with your hardware I guess.