It seems as though the common scenario is to be in a safe computer, and receive prompts for username and password when pushing branches to GitHub from RStudio.
I have the reverse problem. I don't remember how I set it up, but it is not asking for username and password, pushing committed branches automatically.
How can I reverse the settings so as to be prompted every time?
git config credential.helper
If that gives you any output, then you have a credential helper defined, and it could be caching your credentials.
To disable the helper, do:
git config --unset credential.helper
Depending on where the helper was defined, you may need to also include one of
git config --global --unset credential.helper