A casual reader of your post may think that natural moral sense produces something like a universal feeling of human brotherhood whereas religion is a cultural evil that gives cohesion to some groups in order to exploit others.
The fact is that the first can not be true. Our natural moral sense is designed to give cohesion to our group and to exploit other groups as well as religion.
This can not be other way since our moral sense evolved when we were living in small groups of hunter-gatherers. There is no instinctive universal brotherhood feeling. It can Intellectually desired, but there is no biological basis for it.
Thus, your phrase:
assumes that cultural traditions are group-ist, whereas natural moral sense not, and this is absolutely misleading. It can not be anything like and instinctive feeling of universal brotherhood.
What ties Huck with Jim is not human brotherhood, but something that evolutionists call "reciprocal altruism" that has a proximate name: friendliness. reciprocal altruism is a tribal instinct that permits mutual aid.
In this light Huck has a conflict between two tribal groups he is member of: the one he belongs since he was born and the other is the one that he has recently established: his friendliness with Jim. The social instinct caught him in a conflict. both set of social/moral instincts that break Huck apart have pure selfish origins, explained in evolutionary terms.
So I can not admit the idea of a broader scope (in terms of number of people that we consider as equals) for moral instincts than for Religion. If any, i can think about just the opposite. Tribal, uneducated people are not aware of other people suffering. As many modern anthropologist can corroborate, the human condition is usually reserved to the members of the tribe. Pinker mention an African tribe for which the word for "food" is the same used for "out of the tribe" . if there is any human characteristic that can broaden the circle of persons for which we have empathy is culture and civilization. In this sense, the great religions are a cultural achievement against the natural narrow circle that is the default in uneducated people, either in tribal primitive life or in marginal urban areas of the western world.
Finally I doubt that the separation of natural moral instincts and religion makes sense; Any Evolutionary psychologist could say that any cultural phenomenon that is pervasive, universal and reappears whenever it is repressed among different cultures is quite probably the social effect of an human instinct or a set of instincts. If it is so, religion is a part of our natural moral instincts, so there is no reason to separate both. The intellectual disregard of religion would be the disregard of one of our most strong instincts, and this can be socially dangerous.
(trough Lady Godiva, thanks)