I think in other religions that is arguably true as there is the idea that you have to be 'good' or follow certain rules to get to heaven. In Christianity it's recognised that no-one is actually good enough to get to heaven ("For all have sinned and fall short of the glory of God"), all deserve hell ("the wages of sin is death") but God made a way by which we could be saved ("For God so loved the world that...", I guess you know the rest).
I see you focus on the "Love the Lord your God" part, that should be a natural reaction to a God who first loved us and sent His son to deal with the problem of sin, the other part about loving your neighbour is the part which shows that Westboro Baptist Church are not the ones who represent the true face of Christianity. They may believe that homosexuality is wrong and scripturally they have good basis for that but the way they obsess over that and treat people cannot be said to be loving. I agree the church has become too liberal but while we were instructed to spread what we believe (The Great Commission at the end of Matthew) it was never supposed to be my coercion. And if we believe there are eternal consequences to people rejecting God why wouldn't we want to tell others?
My definition of Christian teaching is the teachings of Christ. Simply that. By definition, that's what it is. Old Testament laws need to be looked at in the context of that and as part of an unfolding revelation over millennia. It's not about picking and choosing at all, I just told you what Jesus said was most important.
The difference between Jesus and the other people who claimed they were Messiahs of course is that Jesus is alive and the others aren't. I guess we'll probably have to agree to disagree about that.
I don't think many atheists do try and convert people actually. Some do (I'm looking at YOU, Richard Dawkins), but most are happy to live and let live. And why wouldn't they be? They may think I am sadly deluded but if they're not following any particularly teaching then why should they care? I worry about the ones who seem so desperate to 'convert' people (Still looking at you, Dawkins). What happened to them that it's not enough for them to simply not believe, they have to insist others don't either.
I have discovered from experience that I will never argue someone into faith, the bloke who was preaching on Sunday related an experience when he was talking to an athiest on a plane, they talked for a long time and the athiest had an answer for every point he tried to make so in the end he said "look, can I just pray for you?". The atheist said fine and had a powerful encounter with God. If you're interested I can upload the recording of that part of his talk. It's things like that which affirm my faith - seeing and hearing about the way God has touched people's lives directly.