Someone who comes to find the arguments in favor of one important topic may start looking around and find the arguments in favor of another topic to be (to them) equally problematic. There may be an anti-ecclesial sentiment joining the two as well: the church is corrupt and oppressive and must be gotten out of.
Otherwise, I have yet to see any positive doctrinal connection between them, where one solidly implies the other. (Unitarian arguments of universalism from Christology tend to be pretty similar to trinitarian arguments from Christology, in that Christ recapitulates humanity and/or becomes the federal head of all humanity and/or reconciles all sinners to God by virtue of His sacrifice etc.)
Several months ago I posted a thread asking members to post arguments for universalism from specific doctrinal precepts of unitarian theology (in parallel with my derivation of universalism from trinitarian precepts, or as a few of our members derive universalism from modalistic precepts.) I don’t recall where that thread is now, but possibly someone answered and I didn’t get around to reading it.
This would be a good thread for our U-tarian members to take a stab at it, though! I’ll be curious to see any results.