Consider this.

Nightingales go to Nocturnal her realm.

But vampires go to the Cold Harbour, no?

So what would happen if a Vampire becomes a Nightingale? Well that would be awkward, but I do like the idea of a Vampire in Ancient falmer armor and a Nightingale hood.

It gets even stickier if one has completed a lot of daedric quests.

Would have been cool to see the old Aedric quests available, but becoming a priest/priestess of the Gods of Tamriel seems to have vanished after Morrowind which had the option to join various Aedric Factions.

If the final companions quest in which you free the Harbinger from Hircine is any clue, it would seen one can also break a person's connection to the daedra, if they (the person, not the daedra) are willing to participate.