Even with a god, whether it's a matter of that god actually existing or the individual simply believes in a god, there is no objective morality. Take for example what is considered the most heinously immoral act: murder. According to the big book of biblical fairy tales, Moses gathered up the first draft of the 10 commandments, which included the one about "thou shalt not kill", and came down the mountain. When he saw some of his people had made a golden idol and started worshiping and praying to it--as people stuck in the desert with no food or water or any sign of help tend to do out of desperation--he promptly ordered them all to be slaughtered. Some time later in the book of Numbers their god commanded them to gather an army and destroy the Midianites, slaughtering everyone--men, women, children--except saving the virgin girls to be kept for sex slaves for the men. (Specifically, they slaughtered every man and brought all the women and children back to camp. Moses was pissed that they spared the women and children, so he ordered that all the boys be killed, and that every female who was not a virgin to be killed. All the virgin girls--meaning, children--could be kept by the very same men who had slaughtered their families, which implies they were sex slaves.) Clearly in the bible they think nothing of murdering people. In that same Midianite story they also plundered all the livestock, valuables, and other goods that they wanted before burning the civilization to the ground, a clear violation of the "thou shalt not steal" suggestion (it really seems they were suggestions, not commandments).
In the real world, killing is subjective, not objective. When a killing is done out of spite, greed, revenge, control, etc., it is considered murder and therefore unacceptable and immoral. When a killing is done to relieve someone of terrible illness and suffering, it is considered euthanasia and, at least by some part of the population, is considered acceptable and moral; a mercy killing. In the real world, taking something that belongs to someone else without their permission in order to gain the value of what is taken and/or to deprive that other person of that value is considered stealing and therefore immoral. But when taking something in an emergency situation, such as taking food without paying for it because you have a family to feed but no money to pay for it, that is considered morally correct. BTW, when I speak of morals (moral and immoral), I'm not using it in the common "what agrees with my opinion is moral and what I disagree with is immoral" bullsh!t; I'm gong by the dictionary definition of morals which means that which is truly right or truly wrong based on real tangible benefit or harm to others.
Take some other matters like rape or slavery. In the real world rape is always immoral and rapists rightly get punished by our legal system. In the bible, rapists are ordered to marry their victims, who must then spend the rest of their lives with the rapist. And the bible has no commandment that says, "Thou shalt not go balls-deep into the supple young fart lockers of the altar boys...I'm looking at YOU, priests and clergy!" If that god actually existed and was omniscient, a detail like that would have been in there. In the real world, civilized society is vehemently against slavery and the owning of another human being as property. In the bible, slaves are told to obey their masters numerous times, and masters are given the instructions on exactly how much they can beat slaves (it's OK as long as they don't die within the first couple days), how much they can buy and sell slaves for, how to trick short term slaves into becoming lifelong slaves, and so on.
It rather seems it's impossible that objective morality could exist *with* a god. The bible and other religious texts, and the gods within them, are all absolutely horrible. That is why a secular society governed by secular laws is the most stable and peaceful.