There are "good questions" (related to the topic of Christianity) and then there are "good questions that work well on Christianity.SE"...
These two groups are overlapping but different sets, and because of the nature of the site, the latter set is actually quite a bit smaller than the former set. Why is this so? Well, one of the main reasons is because we wish to avoid one of the problems you mention - people voting based on agreeing/disagreeing with the theological view expressed. Or even worse, questioning the validity of a particular viewpoint to be even represented on the site (This latter problem is talked about in the post Christianity.SE vs. Survivor).
So we wish to avoid the types of questions that will provoke such choices. We may not be able to do this entirely, because voting is anonymous and if people really want to vote according to their theological prejudices, we can't actually stop them. So the solution worked out in the formative period of the site, is to avoid what we call "truth questions". What is a truth question? A truth question is one that seeks to determine whether a particular doctrine is true (or whether a practice is valid) without addressing the fundamental question "according to who?". The problem these types of questions cause, are addressed in the post We can't handle the truth. That would seem to leave a whole heap of things off-topic to the disappointment of many people. However, we can simply avoid the vote-wars, by promoting an understanding of the site's culture that it exists to be descriptive not prescriptive. It exists not to say what is right or wrong, but merely to describe what (different kinds of) Christians believe (about what is right and wrong and many other things); and that does actually still leave a whole heap of stuff that can be asked about.
So what is a good question for Christianity.SE?
One of the first steps to writing a good question for Christianity.SE is to request a specific viewpoint appropriate to the question. Unfortunately, many new users don't seem to understand how critically important this is and write question after question that needs to be radically edited or closed.
That said, here are some posts that give more detail to this and other principles, while providing concrete examples as well: What makes a good focused question? & Types of questions that are within community guidelines.
What I've said so far has been about "good questions" that will fit this site, not about down-voting as such. If a question is not good for the site, you might think it will automatically attract down-votes, but this is not necessarily the case. The appropriate response for a question that is not a good fit, is a VTC (vote to close) and a comment explaining the problem with the question. It is preferred that these questions are closed asap because a) they can be reopened easily if and when the underlying problem is addressed & b) while they remain open in a form that doesn't work well for the site, they are highly likely to generate more content (in the form of answers) that is not a good fit for the site either.
When should we down-vote a question?
There is a pop-up description when you mouse-over the down-vote option next to a question that says:
This question does not show any research effort; it is unclear or not useful.
So while voting is anonymous and we can't enforce that people stick to those criteria, they should be the basis on which people decide to down-vote.
How a person determines whether a question is "not useful" is likely to be somewhat more subjective than the other options; but from my observations, most people down-vote not merely because they disagree with the theological ground of the question, but are more likely to do so if they make a judgment that the question is likely to be controversial without adequately addressing the particular viewpoint requested or they are asking a question of a particular viewpoint but are somehow misrepresenting the viewpoint in question (very common in "gotcha questions").
You should find it relatively easy to avoid down-votes if you follow the site's Guidelines toward a polite, academic tone.
If you are a new user and have managed to read through this post and the linked content in it, you may be wondering "why on earth is this all so complicated? Why can't I just ask a simple question?" To that, all I can say is that this site exists not to answer simple questions, but to be a persistent resource that provides expert answers for well-defined questions - it may not be what you are looking for.
That said, if you learn the ropes, you may find that there actually is a lot of content on the site that is useful to yourself (try searching under some of the tags that are more closely related to your area of interest) - having a good idea of what content is already on the site: will help inform what makes a good question; will help avoid wasted time writing duplicate questions; and will help to identify "gaps" in the site where it would be useful to ask questions.
Newcomers: Be patient. You will get there if you follow our direction. Keep trying.