It is one thing for an opinion to assert that a free republic must allow for freedom of religion. It is quite another to assert that religion is requisite to the existence of free republics. The two, religion and free republic, are not mutually inclusive nor mutually exclusive. They exist as separate propositions with areas of overlap.
One has but to think of religions that do or did practice revenge rituals, human sacrifices (some might also include animal sacrifices), and extreme forms of sin tests and punishments to know that moral behavior and virtue are not inherent in religion. Moral behavior and virtue may not even be said to be inherent in philosophy, consider the philosophy of hedonism.
This being said, I think it is a fair assertion that moral behavior and virtue are requisite to the existence of free republics, consider what happened during the immoral and unvirtuous era of Robber Barons at the height of the Industrial Revolution in Christianity dominated America.
Reason had to intervene in the shape of sound public opinion and government regulation to impose moral behavior and virtuousness with compassion [morality can, has been, and will be legislated]. Perhaps it is just to say that moral behavior and virtue are inherent only in Reason? It seems just to say that Reason is required for a free republic.