Who's talking religion? We're discussing morals, irrespective of their roots or source. There is a possible argument to be made that the fact that this edict against stealing is ultimately beneficial to the potential thief, as it facilitates the functioning of a society he needs, would be rain enough to stop him. However, the consequence deterrent would likely be a much stronger factor, and eliminating that would result in a much higher level of theft.
We might just be disagreeing on semantics. If somebody is not committing a crime because he might get caught, that doesn't make him have morals or act morally (or at least intentionally morally)
The point remains that the only reason somebody doesn't do wrong is:
A. He believes in a Higher Being that doesn't allow it = morals. Ideas about equality or human rights fall into this category
B. He's out to serve himself = selfishness, not morals. "Do not do unto others what you wouldn't have done unto you" falls into this category.