In Betrayal at House on the Hill, what happens when a player owns the Holy Symbol and turns into a vampire?
There are no rules dealing with this specific interaction, so we have to make conclusions based on the specifics of the rules that are there. By a literal reading of the rules, the traitor would be unaffected by the Holy Symbol in this case.

The rule states:


  Each time any Vampire
  tries to enter the Chapel or any room with an
  explorer who has the Holy Symbol, it must
  attempt a Sanity roll of 6+ to enter that room. A
  Vampire who fails that roll can't enter that room. 


In general, to "enter any room with an explorer who has the Holy Symbol" would mean that the room you are trying to enter already contains an explorer who has the Holy Symbol. Especially given that it is talking about "trying to enter" a room. Meaning, before you have entered the room, you check what's in that room. If it is the Chapel, or if it contains an explorer who has the Holy Symbol, you must roll.

In this case, the Holy Symbol is not in that room, because it is with you in the room you are currently in. So you are not trying to enter a room that contains an explorer with the Holy Symbol.

Thematically you can think of the Holy Symbol as needing to be "activated" by an explorer to have the negative effect on the vampire. This would explain why it doesn't effect the vampire if it isn't just sitting on the floor of a room; it had to be with an explorer. So while it's simply sitting there in the vampire's pocket; it would have no effect. 

You can also see it as thematically, it should effect the vampire, because it is a Holy Symbol. If you prefer this interpretation, then I recommend the house rule that the vampire automatically drops it when he becomes a vampire. As Betrayal at House on the Hill is a very theme-driven game, sometimes coming up with rules that make sense thematically is fine. And I don't see that rule as causing much of an imbalance.