I have an iPhone SE as well and have the same issue on all my devices. My issue seemed to start after beginning a new group text mixed with Androids on my Mac. That often creates as glitch and I see that a combination of protocols - RCS, MMS and SMS are being used in the conversation by different individuals.
The fact that I created the group message on my Mac seems to have something to do with it. The group message on my Mac is different from the conversation on my iOS devices. For example, I can't access the Contacts from the thread on my Mac, nor can I change the name and image of the group. This is a new glitch. I tried deleting one of the duplicates, but different versions were deleted on iOS than on Mac OS. It's a mess. The only resolution may be to start from scratch by creating a new group conversation on one of my iOS devices instead of the Mac. I’ll try a few things and update this if I find a solution.