It must be a word used in general context, and not only in the context of religion. Here's the definition from AHD:

To abandon one's religious faith, a political party, one's principles, or a cause. "

Also, as I mentioned above, it appears on over 17,000 Google hits, not all of which on the first three pages are related to religion.

Could one write, "Apostatizing his once favorite party, Henry voted in support of his instincts." Would that be correct usage of the verb?

Second edit: I should have looked more carefully at the dictionary entry. Dr. Bill just pointed out that it's an intransitive verb, so my sentence sucks.So how could I rewrite this sentence: "Apostatizing his once favorite party, Henry voted in support of his instincts." "Apostatizing, Henry voted in support of his instincts and against his once favorite party." Would that change work?