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Settings-apps-all-messages,force stop and clear data. Restart. Make sure you have a backup of your messages before you try.
Do any of you have ultra stamina mode enabled?
You should keep an eye on this topic too:
/t5/Xperia-Z2/Messaging-Not-Working-after-Lollipop-Update/m-p/964383#U964383
It is the same as this.
I am not sure it will help,just told you to keep an eye there too,as the discussion is almost the same. You can try to perform the repair.