When I'm talking about a "god" with a small g I'm talking about whatever mental construct is used in a persons mind as the ultimate goal that dictates if a behavior or event is "good" or "bad", "right" or "wrong". When I talk about religious I mean that a person behaves according to that goal. We all have one, the very basic is just pleasure. If we didn't we wouldn't have a single motivation to move a muscle in the morning. Animals don't get to choose their "god". Humans do. And it is an irrational choice whatever it is.
1) I first choose to believe that my own consciousness is a good thing.
2) I then choose to believe that other's are conscious like me.
3) I choose to believe that consciousness, whatever it's cause for existing should continue to exist (most people take this as an assumed fact, but it is really a choice we all make).
4) I choose to believe that it is good for conscious beings to be happy and not in pain.
The above beliefs are all irrational beliefs, but ones that almost every human shares and is all that is necessary for basic morality. Though it is also evident from daily life that many people make decisions that override #4 in favor of their own happiness, thus their morality ends there. I think that this is the cause of most pain in the world.
Most people do not consider the above beliefs "religious", they just consider them to be a given that we all agree on. I would guess that everyone chooses to adhere to beliefs 1-3. A lot of people also choose to believe in #4. Many would consider themselves atheists as they do not believe in the existence of a deity. But belief in #4 is still an irrational belief and a choice. Albeit one that I agree with. Though what most atheists refer to as the "evils of religion" is when religious people choose to apply #4 to people who follow their religious "god" and do not feel that it should be applied to "infidels" or "unbelievers".
Thus most morality that we observe comes from "beliefs" that people choose beyond 1-3. These morality systems can vary widely depending on the other beliefs that are chose whether or not they are based on a deity or a political ideology or something else (like the good of the planet Earth).