From what I've found in searching this likely applies to other VZW Moto devices but starting here since I've got an XT926M. If mods think it is worthy of a more general forum feel free to move. I couldn't find much here on Droidrzr regarding this particular issue.
So this is an XT926M with the current (final?) 62-15.1 OTA update, rooted and bootloader unlocked, using the VZW frequencies with an account through Page Plus. I do use AFWall+ with a whitelist allowing anything to use WiFi if available but only select apps to use cellular data. I am comfortable with Linux if I need to do something advanced behind the scenes.
SMS messaging works fine. When I'm not on a WiFi network and am online via cellular data only MMS seems to work fine as well, but once I'm connected to WiFi then MMS starts getting problematic. My take on this is better for the incoming picture message side of things since it gives me a bit more visibility. It appears that when the MMS notification comes through via SMS that it actually contains a link to a URL that the phone is supposed to pull down, something along the lines of mms.vtext.com. My understanding is that the phone is supposed to know to route this over the cellular data connection as VZW doesn't allow public internet access to vtext.com, only through the cellular data links they control. (that makes sense, sort of like only allowing traffic through on a VPN) But I found reports online that after an update (the first KK push maybe?) that problems of this nature started appearing with MMS, like VZW pushed an image that no longer had the proper routing for the MMS service.
So, any thoughts on how to make this work properly, short of trying to downgrade? I'm able to get around it by turning off WiFi when I'm sending an MMS message or when I see notice that I've got an incoming MMS, but that isn't the way it is supposed to work. Not really looking to switch to a 3rd party SMS/MMS messaging client but even if I did I suspect I'd encounter the same problem. I'm thinking that being rooted and having AFWall+ installed (and possibly even without AFWall+) that I could include a customization to the iptables to force any activity from the messaging UID to exit the phone only on the cellular data interface (rmnet0 I think?) but I haven't yet been able to wrap my head around iptables rule creation.