Projects can also be mirrored on Github[1], so even if the main repo is somewhere else (e.g. GitLab or Bitbucket) contributors can still be credited via Github[2] and the project can still get the publicity on Github.
But you can't disable pull requests and other features (at least when I last checked) which means you still have to actively manage those. This probably means handing access to the GitHub repo to your collaborators so they can click "close" if hey don't want to merge. Next to "close" there's this shiny green "merge" button. Clicking that not only merges the untested change but also adds a change to the copy which isn't in the master ... really bad.
In the PHP community we "fixed" that by being very restrictive with access to the GitHub repo and provide an extra tool (https://qa.php.net/pulls/#repo=php-src) where any contributor can comment/close PRs via a special GitHub account and GitHub API
[1]: https://help.github.com/articles/about-github-mirrors/
[2]: e.g. https://github.com/dsandler?tab=contributions&from=2015-10-2...