Now, this is a troubling question.
On the one hand, I want to say no, because otherwise all a vampire would have to do to gain immunity is to declare himself or herself without Christian faith. (And I don’t see vampires as big churchgoers anyway, so that doesn’t seem like much of a stretch.) Saved by atheism! There’s an intriguing concept awaiting a screenplay.
Furthermore, I’d have to say no if I want to think that those symbols and substances have any power at all. If any vampire is immune, aren’t all vampires immune? After all, vampire lore and legends in some form are older than Christianity and are also known across many cultures. If the efficacy of the symbols depends on subscribing to the faith they represent, then they are very weak. I thought part of the idea of this convention was to affirm the supremacy of Christianity over all that is on, above, and below the earth—something that the Church never shied away from, even if it isn’t considered politically correct today.
But on the other hand, it surely narrows the definition of a vampire to say that it must be subject to the traditions of any one faith. Vampires must transcend conventional faith, or where is their power to terrify? Clearly they do not subscribe to the tenets of a civilized religion or the morals of decent society. Their very otherness, being so far outside the rules, is what grants them both their terrible powers and their fascination.
One could surmise that any vampire can be subdued by any consecrated object of any faith, but that would be stacking the odds pretty deeply against them, especially when it comes to nature religions that see all creation as sacred, not to say extremely confusing to moviegoers. We would quickly run out of vampires to destroy if everything in nature could melt them down. And then where would the Dracula franchise be?
On the whole I think the wisest course is to display your crucifix if you have one, but be ready with a wooden stake and mallet just in case they didn’t get the memo.