. . .Usually either side can't "leave each other's beliefs alone".
Yeah, I've tended to notice that anyone who makes it a point- however subtle, quick, subversive, "in the closet", etc. it may or may not be- to mention their atheism usually ends up, sooner or later, trying to push their beliefs on others, like we Christians. I'm sure there are those who just don't think about it, but trst me, there are TONS of Christians who "just don't think about it" as well (I call them names like "sunday morning Christians"). But to the actual topic at hand-
To make this quick, let's name some big differences between camps within Christianity. Catholics teaches that the Eucharist actually becomes, literally, Christ; Baptists teach it's just symbolic. Methodists teach that Christ died for everyone, period, no exceptions; Presbyterians teach that Christ died Only for those whom He unconditionally elected. Messianic Judaism doesn't teach that baptism is required for salvation; the Church of Christ does. Seventh Day Adventists teach that the sabbath is on Saturday, period, and to worhsip any other day and not Saturday is a sin; Episcopals don't teach this. WOW! These are major differences indeed! To me, it's unloving to teach election the way Presbyterian Doctrine teaches it. For Adventists and Church of Christers, it's unholy to take a command which seems so clear and just say "it's the spirit of it". Like, dang. What do we do?
I've learned this: are we going to get a theology exam when we get to heaven, and those who answer the right questions are in? "Well", says Jesus, "You got the Election and Baptism questions right, but you were wrong on the Sabbath. . ." *pulls lever, floor opens from under you*. Yeah, you see.
We are told to judge others by their fruit. The more we get to know God, the more clearly we see fruit when it comes up. We DO NOT know who's going were (only God can read hearts), but we can make educated guesses, based on fruit, as to who loves Jesus treuly, and who doesn't. I've known people from all those denominations above, even people who are Mormons and Jehovahs Witnesses, even Muslims and Hindus, who show fruit of loving Jesus with all their heart. Are they going to heaven? I'm not to say. But I can say, based on their fruits, that to all practical and outward appearances, I could and should treat them just like a brother in Christ.
Now as for knowledge, doctrine, I can try and convince people of what I believe to be true, because I think it will better show them God, hence helping them produce better fruit. But in the end, I truely can only be super humble in my judgment, and treat everyone with brotherly kindness, while treating some as Christian brethern, and the whole time teaching everyone the doctrine I feel is correct (being humble, as I said).
I hope this helps.