Among Imperial Romans, religion was pretty much a matter of correct performance of ritual, not belief or conviction. In addition, it was inextricably tied to the well-being of the state, supporting the leadership. If the god or gods you worshipped or your religious practices didn’t stand in the way of the social welfare as a whole or wasn’t viewed as such, it was acceptable (with some exceptions, e.g. the cult of the Magna Mater, early Christianity, and the practice of magic and sorcery). Other than that, Romans were the religiously cosmopolitan sort. You could worship whichever god or gods, follow any Mystery cult, and/or adhere to the teachings of the philosophical school of your choice.
What this means for my perspective on other religions:
What does your religion teach about other religions?
It doesn’t inherently, but as a cosmopolitan sort (much like my religious fore-bearers), other religions are perfectly fine to me. Through my own investigation into other religions, I’ve found that they, each and all, have different things to teach which are of value. Though I don’t possess any extensive knowledge about it — and despite the theistic differences between this religion and my own (Traditional Stoicism) — I, personally, am awed by Judaism.
What does it teach about what will happen to folks from those other religions in the afterlife?
Traditional Stoics don’t really focus on an afterlife, but I’m undecided between a general spirit world/underworld and some sort of judgment in the afterlife.
What does it teach about folks from other religions living among you if yours is the dominant religion?
Again, nothing in particular, but I view human nature as possessing a daimon, a genius (that is, a Divine Spirit within). Just as the gods are benevolent and morally upright, so, too, were we created by God to live as morally virtuous beings. Because of this, I refuse to mistreat those whose religious manners differ from my own.