So I just had this problem. My own device sending ANY iMessage message would cause the recipient to get an image and not an iMessage. So when they tapped the MSMessage Layout image - it would bring up the image viewer.
I was sending to two different people and they were experiencing the same problem but they had both just upgraded to iOS in the last hour, so we thought that was the problem. I ended up testing by sending a message from another device and that worked fine on their device.
I rebooted my device after removing a sysdiagnose profile and the beta profile. And then it worked.
Hopefully this can help your users if it's related.
This morning everyone who had problems messaged me saying that it's all working now. I guessed Apple fixed it overnight somehow.
EDIT: it was just some subset of users but not all. Removing the beta profile helps. Thank you artmin!!