I can't say if this is an issue with Systemd, but in OpenRC systems init tries to start snmpd before it starts dbus. snmpd promptly informs you that it requires dbus to be running, and then quits. I was able the fix this on my system by added dbus and network to the use line of the init script. dbus, obviously, because snmpd specifically says it needs it, and network because what's the point of having a "simple network monitoring protocol" (the definition of SNMP) if you don't have a NETWORK to monitor? After I did that and rebooted, snmpd no longer complains that it needs dbus when it tries to start. Note that while this doesn't seem to be an issue for snmptrapd, I also added those changes to the snmptrapd init script, just in case.
This sounds kind of curious considering net-snmp itself doesn't use dbus at all looking at its code (not that I know this inside-out). Source of the issue may be elsewhere (I can start snmpd without dbus running at all, but that's just my configuration), seeing the exact logs of the messages you're getting could give pointers. If unsure, may be better taken to support channels where it's easier to discuss: https://www.gentoo.org/support/
