TextMate 1 had a preference called "Auto-pair characters (quotes etc.)" that would allow you to enable or disable the auto pairing functionality.
Is it possible to disable this feature in TextMate 2?
You can disable it for a given bundle as explained in this issue on GitHub.
Basically you have to edit an option file of the bundle and add smartTypingPairs = ( ); near the end of the file.
I don't know if this can be generalized using the .tm_properties files but you are welcome to try (and report your results).
There is also a user defaults key for this:
defaults write com.macromates.TextMate disableTypingPairs -bool YES