Given the setting of Forgotten Realms and what happened regarding god intervening. I think every class should be able to pick a god.
In the setting of forgotten realms most people are polythestic. Picking one god's to devote too isn't common at all.
It is rather common to have a patron deity in Faerûn while still praying to varying gods for specific endeavors. A thief who worships Mask might still offer a prayer to Beshaba to avert misfortune on a heist. Most sailors utter a quick prayer to Umberlee before going on a sea voyage, despite their actual patron deities. Having a patron or favored deity doesn't mean someone is ignoring the rest of the pantheon.
