Sort of reminds me of India (the polytheistic "industrialized" society).
Not exact models of what a modernist Rome would look like, though. For one thing the Roman legal system, in its various forms, was a different creature. They had slavery ... but also very liberal marriage and divorce laws compared to most societies in history.
They're also one of only two legal systems which developed torts -- in Roman law, delicts. As an innovation torts/delicts take a lot of pressure off the state to provide regulation of commercial and personal behaviour, because a lot of it is then handled at the lower level by individuals and companies.
Nowadays, the only two major religions that one can say are even remotely monotheistic are Judaism and Islam. The Islamic notion of "tawheed" (unity of God) being a good example of a belief system that is genuinely monotheistic.
In terms of veneration of saints etc; that's mostly because the early church deliberately went out of its way to absorb existing customs and beliefs. Many of the dates in the Christian calendar are pretty much stuff scribbled over the top of an existing pagan festival. Christmas pretty much replaces the Saturnalia, for instance.
It sounds like you're outside your comfort zone. Jesus is not other than God [the Father or God the Spirit] in orthodox [little-o] Christian belief. It's confusing for sure.
Catholicism includes the veneration of saints but they are categorically not gods, nor are relics gods, so how can the inclusion of such elements indicate polytheism.
Interesting that you mention Islam as one of the criticisms of Islam is that many supposed adherents appear to worship Mohammed as a god, certainly as much as Catholics "worship" the beatified. There is also the notion, warned against in the Quran IIRC, of worship of the djinn which could be considered analogous in some ways with veneration of the saints.
As for veneration of saints and relics, then anything that worshipped is a god and asking for blessings, intervention in worldly affairs, etc are all acts of worship. So when someone prays to a particular saint seeking something they are engaging a polytheistic act just as one who prays to an idol is engaging in polytheism.
I am not sure about Muslims worshipping Muhammad. Maybe in some polytheistic branches of Islam such as sufism and so forth which were themselves influenced by hindu/christian/etc ideas.
For those that don't consider the Brahman to be personal, and some that do, then within their philosophy [or practise] there are certainly distinct gods with distinct beings.
Not everything that is worshipped is a god. You can certainly worship something which is not divine - one of Jehovah's big beefs (!) with the early Hebrew tribes was their tendency to make things to worship.
When Catholics appeal to dead "Saints" (quite contradictory to NT use of saints to mean those who believe in Christ Jesus and so are saved) they ask for them to intercede before God for them. The thought is that the Saints are in heaven and so have the ear of God in a way that mortals do not - that is not deifying the Saints. It is not polytheism in practise or reality.