In the D&D world, the gods are real. There is proof that they exist, they grant Clerics and other divine classes powers like a pez dispenser.
How would this affect the religions associated with these gods? Such a large part of religion in the real world is about faith- faith that [insert deity] exists and that they do and act the way that [insert corresponding holy book]. But what happens when we know that these deities in fact exist and that the do indeed act according to what their holy book says.
I think that they faith aspect is still relevant to a certain respect. The followers still need to have faith that when they ask for their god's aid, that they will grant it. The cleric still needs to have faith that his [insert divine spell] will work, otherwise he probably wouldn't go out adventuring if he feared his god granted powers would suddenly be gone. There is still faith involved, that their god will not change his mind about his morality and one day decide to turn evil or something. The faith becomes more similar to the faith people have when they are in a relationship rather than a faith that the god exists or not.
Other than faith, what would be different? I think that there would be a number of people against religions because they don't like the idea of worshiping and bowing down to another being, even if that being is by any measure far superior to them (think stargate SG 1)