There are 6 responses your comment and not one has mentioned that both hg and bzr have full interoperability with git. I use github extensively with both bzr and hg, and haven't used git in a while. Your personal choice of SCM is entirely irrelevant to which web service you use.
Can you tell me how you use hg with github? I really prefer working with mercurial but have often switched to git for projects I want to put on github. I know there's some git plugin for mercurial but I thought that was old and unmaintained?