Whether they believe in God or not is irrelevant to the truth of His existance, and to the necessity of His existence for the existence of morality & right and wrong.
In other words, no, you don’t have to believe in God to have a sense of morality, but God does have to exist for you to have one. The two arguments are independent.
Now, what are you gonna do about doing what you know is wrong and the knowledge of judgement against that object standard?