I have no doubt that religion gives an easier recipe for being moral, or to put it less ambiguously, for doing the right thing. It's just easier to follow, little to no thinking involved necessary. However at least in the West we mostly have secular societies, who have thrown some of those religious dogmas away a long time ago, even punishing some of them by law.
How up-to-date is religion? The major religions are very old, and religions are very rigid. Society changes its norms much more quickly. Certain very basic things can't change, so one doesn't need to look at don't kill and don't steal. The problems lie more into punishing what's inappropriate on a much less basic level - because what's appropriate today is very different to what has been a couple of decades, let alone thousands of years ago. We certainly view as extremism a case of muslim father who had his daughter killed because she wore revealing clothing - but even in Western society, while not killed for that, it hasn't been acceptable for all that long at all. On the same line is rewarding what society has come to view as inappropriate, or teaching it.
The other big problem is the mixing of cultures. Freedom of religion is fairly new as well, and many religions aren't so tolerant of non-members. People in our societies have to learn to live and let live, accepting that others can have different, sometimes opposing, beliefs. Different and opposing are some of the most fought over things and religions never particularly embraced them either. Some people can't live by the "good" (maybe easier to say merciful and compassionate) half of the laws in their holy books.
