The Demiplane of Dread is insulated from outside forces. Outlander clerics no longer feel close to their gods, but their spells continue to function, care of the Dark Powers.
Whether the native gods are real is up for interpretation, barring a couple of definately fake ones (though they still have functioning clerics, go figure).
Native clerics have never felt as close to their gods as Outlander ones do before coming to the Mists.
Clerics and Divine Champions do not unknowingly serve the interests of the Dark Powers, at least any moreso than we all do. Isolation from the gods is a necessary conceit of the gothic horror setting; it is about men and the choices men make, not gods. The Dark Powers stepping in and continuing to provide spells is, therefore, another necessary conceit, to make clerics actually playable.
Furthermore. When a cleric's Alignment or actions deviate from the Alignment of their Deity, usually they'd be cut off. Not so in Ravenloft. A cleric, paladin or divine champion in the Demiplane of Dread continues to receive spells, and by extension, the 'approval' from their deity, 'validating' their skewed or perverted dogma.