Yes, they can and do serve the purpose of social integration.
That said, I want to clarify your argument. You are arguing all religious belief is the same because the choice to follow a given religion is based on the cultural context of a child's upbringing, correct?
Normally that plays a pretty big role in what religion a person considers themselves to be a part of for their entire lives. Whether or not they're a true believer is a different story.
I'll respond to the rest later today.