Actually, I believe the Baptist would say that they are saved because they fall into the category of children; i.e. they aren't able to determine right from wrong (which means they are considered 'saved' by default).
That makes it sound like they don't really believe in ancestral sin.
AFAIK they don't believe in original sin, at least in the way that it is traditionally taught. They have their own belief that all babies go to heaven until they reach the age of accountability (or age of reason). It's a novel little doctrine...
I'd like to know how they really explain it. "Jesus loves the little children" is what they hear for several years, then suddenly one day, it's "Repent or burn in hell!" I've never quite figured out how they decide who is accountable and who isn't. Seems rather cruel to me.
Of course, a lot of child evangelism is of the highly emotional type: "You want to be a good little boy/girl, don't you, and make Mommy/Daddy/Grandma/Grandpa happy, right? And you want to go to heaven when you die, don't you, so you can see Nanna and your baby sister who died before she was born?" With that emphasis on death at an early age, it's no wonder kids have nightmares.