Here is my take:
- Flag as Not An Answer. To boot that attitude is not welcome here. Mod or community delete¹.
- Flag as Not An Answer. Give 'em a newbie help link. Mod delete¹.
- Give the kid a cookie. «— This is where SE lives and the vote system does it's job.
- Flag as Not An Answer. Remind them about our guidelines. Mod delete¹.
Obviously your question is mostly aimed at #4, so I'll skip talking about the others.
To some extent we do already deal with these as NAA. We talked about this in the early days of the site and agreed answers should match the scope of the question:
If this site is going to succeed, it is absolutely essential that questions be answered specifically within the context of the belief system they are asked. This is not optional or reserved for the people you agree with; It is a basic tenet of the site.
As for as the SE network goes there are only a couple sites out there with stricter enforcement of such a a policy (Skeptics, Software Recs, Biblical Hermeneutics, and a couple of the "hard" science sites). However it is still one of our biggest problems. Historically, this is where most newcomers to this site struggle, and honestly I think our biggest failure is actually in not cracking down more on this issue.
On a case by case basis, it seems like an innocent problem. Whoops, they just missed the "LDS" target an gave an "Evangelical" answer. No blood no foul right?
If you step back and look at what that does no the site (on a case by case basis where these have been allowed and on a wider scale like homepage trends), these are really a problem for us.
They attract more of their kind. In your scenario it's not long before another visitor comes by and disagrees with the way the Evangelical formulation of the Trinity was presented and wants to give a more accurate answer. This breeds more answers. Sooner or later (sooner in the case of Trinity questions, later in the case of many others) this always leads to more off topic answers. People come here with a forum mindset where threaded discussions wander from topic to topic. If they read through a couple answers and one of them goes off on something about the Trinity they thing they could explain better, they are going to and completely ignore the fact that the question was about LDS.
They attract debate in comments. This is actually most noticeable between less divergent groups because they assume the other answers should be comparable with their own and are less likely to notice that they are in an apples to oranges situation, but answers that don't match the perspective requested in the question almost ALWAYS are catalyst for ongoing stings of debate oriented comments.
They turn everything into a vote war. Allowing these answers to stand invariably turns perfectly good question into exactly what we are trying to avoid with our "No Truth Questions" policy. You suggest that the community should be able to deal with these by voting on them, but the fact of the matter is they don't. Not only does this not produce a clear distinction between answers that match the question and ones that do not, it doesn't even come close. We simply do not have an educated user base that knows what to vote on and does not vote on agreement with the theology.
I'm not talking about an off balance equation here. This isn't a ship that almost floats and just need some bailing. This is a rock. And not dealing with this is totally unfair to every minority we claim to welcome. If we're going to say we allow question about all perspectives, it's jolly unfair of us to allow the answers to fill up with posts that support the most popular views by number of visitors, which is overwhelmingly non-description generic Protestant (that might not even know enough to know what makes them Protestant). I'm sorry if that sounds disparaging, but that's the spade I see.
On the other hand our voters do fine when presented with answers that are on equal footing. When all the answers are answering the same question, the voting system works great. The Stack Exchange platform works wonders in this department and the best quality and most accurate answers usually get to the top and others end up at the bottom.
As moderators I think it is our just to foster an environment and enforce guidelines that play to this system's strengths. I adamantly believe that for this to happen moderators should not be moderating based of their doctrinal beliefs just like nobody should be using that as criteria for votes. In order for this to work, however, we must moderate based on scope of questions.
If we do not insist that answers that do not purport to represent the perspective requested be removed, we make it much harder to moderate the problem cases and this whole places turns back into "Survivor".
I don't care if it's LDS answering an Orthodox question or Evangelicals answering LDS questions -- either way the main thing keeping this site from falling apart at the seams is setting boundaries:
If you are more inclined to resent rather than celebrate the differences between us, then this may not be the site for you. Our differences are more than divisions between us, they are boundaries that define us. I think there are more boundaries than is necessary, but the only hope we have of crossing them is to identify and respect them.
I think the only hope for this site is to stick to our guns and insist that ALL answers at least attempt to respect these boundaries and match the scope of questions. This should include flagging ones that do not as NAA and deleting them.
Depending on the situation of the user we can redirect them. In the case of innocent mistakes we can educate them with comments and meta links on why their answer is a miss-fit. We can help them find (or even ask) questions where their answers will fit. As the mistakes become less innocent and more blatant attempts at fixing "somebody is wrong on the Internet" by providing what they think is the right answer no matter who the question was targeted at, our education and redirection can switch from newbie directions about how we are different to more directly explained reminders about what were here for. Follow that scale down the road a bit and you end up at #1, which we started out in agreement on so I won't follow that rabbit down the hole.
Occasionally it has happened that somebody whose answer I've deleted accuses me of moderating based on content and deleting their answer because I didn't agree with. The hilarious thing is how little these people know about my own theology. As mainstream Protestants are the worst offenders by volume, often I've deleted things I agree with. I've been accused of being in league with the Pope in a plot to undermine Protestants (by somebody who didn't like their non-Catholic answers to Catholic tagged questions being removed). Several times. I've been accused of being a Mormon. I've been accused of being a Jesuit. I've lost track of all the things I've been accused of being for deleting answers that didn't match the question scope.
The point is, in none of these cases is it really about my beliefs. That is not the factor in deciding whether an NAA flag is warranted or not. If the question asks for X perspective and they are given Y instead, it's NAA in my book. If they attempted to give X perspective but just happen to be wrong (or do a bad job of it), then I leave the post, decline the flag, and usually DV.
TL;DR: We cannot be fair to the broad spectrum of traditions we claim to allow if we don't allow their identities to stand. If we're going to allow LDS questions to be filled up with Nicene answers (whether innocently or deliberately) we might as well just say they aren't welcome here. If we're going to answer Catholic questions with nondescript Protestant personal exegesis, we might as well tell them to get another site. Deleting anything that does not both recognize and respect these boundaries as NAA is the only fair thing we can do.
¹ For situation #1, 3 high rep users can vote to delete downvoted answers. This works well enough for situation #1 as those deserve to be downvoted, but it doesn't work very well for #2 as those answers don't necessarily deserve downvotes, and certainly not for #4 where they often get upvotes from folks agreeing with the theology in spite of being out of place.