I had a problem SENDING MMS messages, not receiving them. Here's what worked for me - don't know if it will work with the RECEIVING problems you all are having. Anyway, you might want to try it anyway.
1) Do a fresh iCloud backup
2) Go to Settings, General, Reset, Erase All Content and Settings
3) When you go through the setup process, DO NOT RESTORE FROM BACKUP - set up as a new phone
4) Once you're through with that, try sending a few MMS messages (send a pic to an Android user, send a text to a group containing an Android user, something like that)
5) If it works, then Yay! Only now should you sign in to your iCloud account. It will take several minutes to repopulate your phone with your iCloud data.
6) Since you didn't restore from a backup, you will now have to re download the apps you want. Open the App Store, click on your name/image in the upper right corner. Then click on Purchased and re download the apps you want. It's been hit or miss for me on which apps will have saved data. I lost game progress for instance, but texting was way more important for me.