As many people already wrote in comments, this is not about MMS, but about a bug in the multimedia library, so disabling MMS will only help to avoid your phone being hacked, when you do not use it, but keeps it turned on and connected to the cellular network.
If you use your phone, you could still be hacked through web browser or ANY OTHER APP, that works with multimedia.
I provide a full answer here: Stagefright security issue: what can a regular user do to mitigate the issue without a patch? on android.stackexchange.com since this question is a duplicate of that one.
Answering the original question, there are 3 ways for common user (if common means that user is not able to root his phone and/or install CyanogenMod on his phone) to protect:
1) Disable auto-retrieve of MMS, install Firefox 38+, and maybe MX player (and disable use of stagefright there). Delete all other applications on the phone including Facebook, Twitter, E-mail, etc. wherever any multimedia content could be. If it is not possible to delete, for example, an E-mail app, just delete all accounts there, so that nothing will be downloaded from the Internet. Now it is possible to use the phone for web browsing, calls and SMS.
2) Turn off the phone, and buy another Android phone with stock Android from Google (e.g. Nexus)
3) Install update if it is available. If not, please select from options 1 or 2.