I discovered that by disabling IPv6, MMS wasn't working for me.

Thankfully, mmsdtng has a debug mode (mmsdtng -d) that revealed it wasn't able to resolve names. Yet I can resolve names just fine on my shell sessions and elsewhere!

It turns out that the the way dbus, which mmsdtng calls, resolves names is directly passing in the interface in question. So for the modem, it would be wwan0 and no DNS configuration was set for it in resolved.

After adding the necessary configuration (allowing wwan0 to resolve outside of wireguard), MMS started working for me!