the one side basically says "do nothing wrong and you'll get to heaven" versus "serve as a member of the church and then you can get to heaven"
Eh, not quite.
From a Baptist point of view it's more like "You've already done wrong, and nothing you can do is good enough to earn your way into heaven, but God provided a way to get forgiveness if you accept it."
Doing good works are not strictly necessary, but every preacher I've listened to has said that they should be a natural part of your faith. That if you're a Christian and you're not helping others, then you might want to take a long hard look in the mirror and ask yourself if you really are one.
Of course other denominations are different, like I know the CoC believes you have to do good works or else you can lose salvation. Then there's also the question of how many people even care at all, and just go to whatever church they grew up in simply out of habit and to see friends.