It's very easy to have morals absent religion. Religion gets its roots from nature. Look at the 10 commandments. At their roots, many of those (the ones not dealing with God, but with daily life) aren't "rules to live by to be nice to people", those are "rules to live by to further species survival".
Don't kill each other. Stick to your own wife (because if you don't, I'll kill you). Don't steal from me (because if you do, I'll kill you). The rest follow the same pattern.
They encourage society to get along and work together. Some people think it's because that's what God wants. And, they might be right. But, I can just as easily view them as ensuring mankind's continued existence.
So, it's very easy to have morals without religion. Basically, do things that will make our group (define group as a family, a neighborhood, a town, a city, a state or all mankind) better. From neighborhood watches to trash pick up days, all the way to stopping wars. They all boil down to being nice to each other. And, that sentiment transcends any religion.
Look at it this way. Animals have morals. Dolphins know not to kill each other, to care for each other's young, and to socialize within limits. But, they don't worship at any altars.