I agree that religion has a place in this debate, but I don't think morality is inherently about religion. I'm not religious, but I do consider myself moral.
I don't know precisely where we get morals from without religion. Clearly it can't be as simple as what the majority prefers: the phrase the tyranny of the majority refers to the problem with that.
We have a deep seated sense of fairness, even without religion. A recent experiment put two monkeys within sight of each other. One did a task and was given a piece of food, then the other did the same task and got a much tastier piece of food. The first does the task again, and again gets the low-value food, but this time he threw it back at the experimenter and beat the bars of the cage, trying to reach the high-value food. That sense seems likely to be where our concept of morality comes from.