You are to some degree conflating theists with people who follow a religion. There are many who believe in God but are not religious adherents (and more every day).This might be a separate thread, but we could turn this around and ask the theists:
Is your religion consistently moral? My experience is that all the major religions offer a set of morals that might have been state of the art 2000 years ago, but which are no longer the best moral ideas available. And so reasonable theists are left to cherry-pick their religions for the bits of morality that are still valid in 2014.
Examples: Christians and Muslims are both instructed to kill adulterers, the RC church behaves in ways that prefer AIDS to condoms, many Muslims think apostasy should be a crime, and both religions - even in modern times - often cry "blasphemy" in opposition to freedom of expression.
So, where do theist "really" get their morals?
But you are also wrong about Christians and Muslims being instructed to kill adulterers. The "fun" thing about religion is that it provides great opportunities for people to read scriptures in any way that suits them.
I'm not a Christian, but the way I read the Bible says that there are two fundamental commandments and that anything which appears to contradict those laws is false:
Those two commandments both say that love is fundamental and nothing is true unless love is the foundation and expression.Matthew 22:36-40
36 Master, which is the great commandment in the law?
37 Jesus said unto him, Thou shalt love the Lord thy God with all thy heart, and with all thy soul, and with all thy mind.
38 This is the first and great commandment.
39 And the second is like unto it, Thou shalt love thy neighbour as thyself.
40 On these two commandments hang all the law and the prophets.
Of course others read scriptures differently.
My thought is thus that whether or not one believes in God or follows any religion, essential morality comes from the nature of being human, the human heart or human soul depending on how you express the thought.