In all my years playing, I never knew the AI had favourite religions. What does that even mean? What does it affect?
Due to attached techs, it can give them a stronger prevalence to beeline that tech -- especially if they have no self-founded religion of their own yet. It really doesn't mean that much, as Religious AIs are gonna Religion anyway, but technically an AI like Izzy is gonna push harder to Theology, in terms of tech weights, than an AI like Asoka.
Also AIs will work to spread and swap into their favored religion if possible. You won't see this much though unless they found none of them, or found multiple but their favored religion is one of them. Izzy is again, a good example, as she can swap to Christianity after Buddhism with little warning even if she founds both or neither of them.
In practice, turning on Choose Religions would in theory cause less religion-founding tech beelining, especially in the crowd that doesn't normally have Religion as a tech flavor.