If you’re using Google Hangouts as your default SMS client, here’s how to protect your device from Stagefright by disabling automatic downloading of media files sent via MMS:
stop stagefright exploitation by disabling auto-download
Prevent Stagefright infection by disabling auto-download

Here’s how to protect your phone from the Stagefright bug if you’re using Google Messenger (the default SMS client for Android 5.0+):

disable MMS in Android to avoid Stagefright bug
How to disable MMS to avoid Android Stagefright bug