No. Please don't. But technically we can't stop you either.
Voting on SE sites is strictly a personal affair. Your reasons for voting are your own and the system cannot tell why any single vote is cast. The system is only useful for its for the aggregate of many votes. Some of the individual votes will undoubtedly be for the "wrong" reasons, but if enough people vote for the "right" reasons the crowd sourced result will be useful in spite of the noise.
There are a few voting patterns that the system will catch. If you vote the same user up or down too many times the system might note this as problem case. This catches both contrived voting rings and revenge voting sprees that would otherwise skew the results. You also have a limited number of votes per day and downvotes cost you a little rep. This encourages you to make your votes counts and discourages new users from downvoting too much before they understand the system and what attributes to vote on.
What have done is come up with question scoping guidelines that make such voting unnecessary. The kind of question you describe would actually be close here pending edits that scoped it in a way that such voting patterns would not be necessary. We really voting to be done on quality, usefulness and accuracy in describing the view represented, not doctrinal agreement. To make this possible we require that questions are framed in a away that discourages "doctrinal popularity contest" style voting. Consider an example:
Question: Does God the Father have a body?
Answer 1: No. God is spirit, but God the Son did take on a human body.
Answer 2: Yes, God had a body just like Jesus.
Answer 3: It was made out of spaghetti.
This pattern is hugely problematic for the SE format. We might all agree on #3, but the voting on the first 2 answers will quickly start showing a doctrinal bias. Basically this example would turn into a popularity contest between mainstream Christianity and Mormonism. Not constructive.
Instead we would put that question on hold until it had a scope that was answerable in a constructive way that would not lead to popularity contests between what different groups believe to be true. Like this:
Question: What sort of body does the LDS church teach God had?
Answer 1: God had a sort of ethereal body that you could see but not touch. It gave off a green light.
Answer 2: According to Joseph Smith, God once had a body of flesh and bones just like we do now.
Answer 3: God does not have a body! Mormons are wrong.
Now it becomes much more apparent what to do. The question here is about what a specific group of Christians believe and answers are expected to properly represent that view. A good answer could even include references to official statements that backed up their case. Even though I believe the view to be heresy I could vote up #2 as I know it to be a more accurate representation of the view requested by the question. #1 becomes objectively a poor answer whether you agree with Mormons or not and #3 can be flagged as Not an Answer and removed entirely because it does not fit the scope of the question.
