That wasn't an attempt to support that point. As a move, it was a backing up, followed by a re-iteration of my initial claim. I realize that I haven't provided evidence; I've only gestured that there's a mound of historical evidence over there to support my claim. Maybe I'll give it another go....
Nothing polices the boundaries of meaning and truth like Gods. And nothing narrows the catchment of meanings further than ONE GOD. (My favorite example of this is the oft-repeated Islamic tautology "There is no God but God!").
The early Roman empire was polytheistic, and, generally speaking, policed the boundary between public and private more than it did the boundary between True and False. You could publicly worship whatever god you wanted, ascribe to it whatever demonstrable forces and signs you saw fit, but common sense dictated that approval from that god depended on accurate observance of rituals. This, at minimum, required that the god have an image and a public alter or temple. Requests/prayers were presented to the god in terms of a trade. A priestly cast emerged to oversee these things, which were very much a part of the State, and gave those trades the force of contract/law. Historians agree that, relative to the way we think about things today, the view of religion was very practical: if you asked the gods for something, and it happened, then you owed a debt (food, wine, animal sacrifice, etc). On the private side, you had the power of the paterfamilias, which, by today's standards, had an extreme grip on the expression of family life. The father oversaw private worship, and the public judiciaries had no power to intervene. Families were microcosms of the State. Theoretically the father had the power to execute family members.
You'd be correct in pointing out that the seeds of fascism are everywhere in this "cultural backdrop"; the insistence on publicity did narrow the catchment of possible practices and thus possible meanings/truths. But, vis-a-vis monotheism, people nevertheless had much more conceptual latitude for framing the essences of humanity and nature. Every single judicial history of a monotheistic State backs that point up. In early Rome, as long as you "registered" your meaning, then everything was cool (one of the most subversive things about early Christianity was it's insistence on meeting in private, and for not playing the game of images).
EDIT (TO CLARIFY): In terms of freedom/persecution, Roman questions about religion and meaning were dominated by the hows of worship. In monotheisms, the questions are dominated by the hows, whys, and whats. You can feel the difference.