Rebasing remote branches in Git
Nice that you brought this subject up.
This is an important thing/concept in git that a lof of git users would benefit from knowing. git rebase is a very powerful tool and enables you to squash commits together, remove commits etc. But as with any powerful tool, you basically need to know what you're doing or something might go really wrong.
When you are working locally and messing around with your local branches, you can do whatever you like as long as you haven't pushed the changes to the central repository. This means you can rewrite your own history, but not others history. By only messing around with your local stuff, nothing will have any impact on other repositories.
This is why it's important to remember that once you have pushed commits, you should not rebase them later on. The reason why this is important, is that other people might pull in your commits and base their work on your contributions to the code base, and if you later on decide to move that content from one place to another (rebase it) and push those changes, then other people will get problems and have to rebase their code. Now imagine you have 1000 developers :) It just causes a lot of unnecessary rework.
It comes down to whether the feature is used by one person or if others are working off of it.
You can force the push after the rebase if it's just you:
git push origin feature -f
However, if others are working on it, you should merge and not rebase off of master.
git merge master
git push origin feature
This will ensure that you have a common history with the people you are collaborating with.
On a different level, you should not be doing back-merges. What you are doing is polluting your feature branch's history with other commits that don't belong to the feature, making subsequent work with that branch more difficult - rebasing or not.
This is my article on the subject called branch per feature.
Hope this helps.