I generally agree with you. Morals are necessary to keep society running smoothly; however, I certainly don't think that every person can adhere to every moral, of course. Morals have too many variables (religion, culture, background, and the list could go on and on).
Some people in religions decide they will pick and choose what morals they will follow. One has to ask, "are certain morals false?" I certainly believe so, just consider some that certain cultures and religions that institute some morals, I find some quite out there; however, they are very real and valid to others.
Also, morals can be relative--one act can be wrong for one person and conflict with their beliefs while the same act would not be viewed as immoral by someone else based on their beliefs--to each person, there is validity in their stance.
Also, something that I always used to think about was the difference between the morals people claim to adhere to compared to which ones they actually adhere to in private. I went to church when I was younger and a major thing I observed was the difference between how people acted depending on their setting and "who was watching" and this was not just the kids/teenagers--this was the adults too--they can be very different depending on the company they are in--very two-faced.
Specific morals depend on the person; for example, some peoples morals just consist of respsecting humanity, while others have morals that are linked exclusively to religion.
Then, people start to question the exact parameters of a particular "moral" and as we know the list can go on and on: is it always wrong to lie? is violence ever ok? when is that sperm and egg actually a human? for some religions: is it still considered "pre-marital sex" during the engagment period, or do you have to wait until you have a marriage certificate in-hand. We can't begin to really define every moral situation and some things will be ok for some and not others. everyone can have different perceptions.