Sounds really similar to my MMS never appear if mobile data are activated *after* the reception (FP3+).
Glad to see I’m not alone.
See my posts; there seems to be a missing togglable option in our settings or something. 
I really want to sing praises for /e/ and Fairphone, and each day I find new reasons to like my new phone, but as long as the holy triptych of SMS / MMS / calls is not stable, my friends will have reactions like “sounds like a chore” or “crap” (that’s basically what they are saying right now, seeing me struggle to fetch my MMSs, which worked just fine with my first, non-smart phone).
Good luck to the devs. Wish I could help but I mostly deal with non-mobile stuff. And Bash scripts (
). xD