the god was, was immaterial. The purpose of the god was to add symbolic force to a set of rules that the authorities of the day deemed useful to society.
The Ten Commandments, which many Christians claim is the source of laws, does something similar. The first three or four (depending on the version you choose) of the Commandments establish God as the giver and enforcer of the laws, and the remainder are rules that serve the purposes of the society regardless of the nature of God, or whether he exists. God (or a god, or gods) are the symbols which validate the rules they are said to establish.
Take away the symbol (God or the flag) and the order that it stands for tends to remain, because it serves the purposes of those who advance and revere the symbol. That point is often forgotten by atheists who argue against the existence of God, and against strictures alleged to have been put in place by Him. It’s not about God; those strictures are there because believers want them there. It may be important to believers to defend the symbol, just as it may be important to patriots to defend the flag. But neither symbol is essential to the underlying order it represents.
Of more importance is that underlying order. Is there a problem with the way the government relates to its people? Changing or eliminating the flag does not fix that; a Constitutional amendment may. Is there a problem with the rules God is said to have established? Changing the rules is far more important than changing or eliminating God.
There is, of course, one major difference between the flag and God. The flag is a passive symbol; it is not said to cause rules or relationships to come into being, but God is claimed as a source for rules. That fact gives some sense to the atheist notion that belief in God has to be undermined to effect social change. Even so, Christian activists are quick to point out alleged injuries to society caused by a violation of God's rules - which shows that they believe there is a secular justification for the rules apart from the fact that God stated them. The rules would be needed even if there were no God.
Changing God is not a requirement to change His rules. We have seen, over the centuries, great changes in the rules said to be given by God. Dietary restrictions have been eliminated gradually – it was only in 1966, for instance, that mandatory restrictions on eating meat on Fridays were relaxed for Catholics. Slavery has come to be seen as an abomination, despite its earlier reliance on God for justification. Segregation has become seen as not desired by God, despite earlier invocations of the Curse of Ham. Tolerance of other religions has greatly increased in many (sadly, not all) countries, and attitudes towards varieties of sexual relationships are changing rapidly in many places.
All without changing or doing away with God. God, it seems, is adaptable once the opinions of society change, claims of "eternal rules" notwithstanding.
Symbols are important, and symbols – particularly symbols alleged to be active participants in rulemaking – have force. It’s not that they should be ignored in a quest for social justice or reform. But it is wise to remind ourselves that they remain symbols, and that it is the underlying order they represent that is at issue.