Indeed, the acknowledgement of God is not synonymous with religion.
But I have made no plans to run for any office right now.
Worship With Your Vote.
The basic premise of the Constitution was a separation of powers and a system of checks and balances because man was perceived as a fallen creature and would always yearn for more power.
Without God there would be no freedom to believe what you want.
False religions like Islam who teach that you must worship this way, are completely opposite with what our First Amendment stands for.