It is rather a difficult question to answer without writing a hub, however, I will put forward my answer briefly.
Basically, you are saying which comes first Chicken or egg?
Morality- If you understand the principle that every human being is linked from before birth to the Spirit of God, you will then understand that every human being is also linked to God's principles of Morality and the existence of God the Creator!
Once a human being is born their environment, experiences and nurturing as well as their genetic make-up determines their pathway in life. Each individual has the ability inside of them to accept or reject God's way of morality and faith. However, if the individual chooses to reject God's pathway (the narrow path that leads to eternal life) those initial traits then remain dormant in the subconscious and only surface again when a tragedy or crisis or some trigger brings those traits back into memory. You can see then, how religion (created by man), feeds the inner subconscious needs of man to continue his link to the unknown Creator God.
Atheist will say they do not believe God exists yet will spend their lifetime trying to convince themselves, and others, of this!
Therefore a person is able to have moral understanding without knowing God.
What I am trying to say is this:
Morality can be used as a tool to hide behind, morality is useless without the affinity to God.
True Morality and Faith (as opposed to religion which is man-made) come from our relationship with our Creator God, through His son Yeshua (the ultimate Torah Law) and God's written Commandments, which is our guide to morality and faith (rather than religion).
Morality and faith is meaningless without God who is the conductor of both!
Therefore it is irrelevant as to which comes first 'morals or religion', as both lead to nothing, without God!
Man's morality may differ considerably from God's expectations from mankind.
An atheist may exercise moral behaviour, (not all atheists are criminals or deviants!) Atheism is also a religion but has little to do with God except to rebel against him by denying his existence!
In 2 Timothy 3 God tells us of the lawlessness in the end times, it mentions all the characteristics of most people in these days - and it is so accurate! It also indicates that morality doesn't exist anymore and religion is false!
Society rejected God's laws now we see the consequences!