Okay, let me see if I can respond to everyone.
@THE, I suppose that discussion over ideology and beliefs is still possible, but, eventually, you realize that you simply morally disagree on certain things and, without evidence, there's nothing more to it.
@SamuelRSmith, I know; I was just using "both" to simplify the argument. Your logic, though, is, largely based on your moral view of things. If I just say that, for example, I believe in evening out the income levels, I'm not sure the discussion can go any further.
@insomniac17, I think you're misinterpreting my problem. My main focus is not "finding the truth", the truth in terms of evidence is only useful here as part of an argument to support taxes/teaching evolution/whatever. And, actually, I rather disagree that I should look for the most logically consistent belief. I'd agree that, from what I've seen, libertarianism/anarcho-capitalism is very logically coherent. The thing is, though, that consistency is a very secondary priority for me compared to, say, preventing people's deaths. I'm afraid I'm willing to screw all consistency if I believe it would lead to fewer people dying.
@Mr Khan, while you're offering me the answer - scientists are trustworthy (for hard sciences) - on a silver platter, I'm not sure why I should trust you on this. What if my local churchman says that he's trustworthy and that he's not biased? What to do then?
@Soleron, but if I don't understand the data, what's the point? I could just read a well-written pro-Creationism argument instead and be equally convinced of it since the evidence - the thing that holds scientific theory above random stuff - is Greek to me.
@dsgrue3, for evolution, while I'm personally in a situation where non-evolution arguments can't be taken seriously, for someone who is religious and has some sort of faith in people who are against evolution, this can't be easy. Your saying that these people haven't been reliable just opens another can of worms here. Also, I've heard people on here say exactly the opposite thing about taxes during a recession, so I'm not sure why I should believe you're more reliable.

I mean, we could get up into some ol' post-positivist shit here, but largely empirical facts are empirical facts. You can look up the experiments, you can (if you have the means) replicate them. It requires you to get informed about things, certainly, but as far as some of the more controversial parts of science goes, that isn't too hard. Learn what has impacted, say, earth's temperature in the past to learn whether you think the arguments for anthropocentric global warming seem to pass muster, or look into theories on natural selection and genetics.

Especially in the modern days of the internet, it's easy to find these things and see them explained in relatively easy ways to follow.

I know tons of religious people who believe in evolution. TONS. Their dispute isn't with the evolutionary concept itself, but micro/macro. They agree that small changes within a species are possibly, but disagree with any macro changes (those being the ones that would involve the evolution from chimp to human creating an entirely new DNA species). Little do they know, microevolution leads to macroevolution, so they are essentially admitting it.

Taxes during a recession as good? I'd love to hear someone's rationalization on that. Maybe in a socialist/communist nation where the taxes are weighed according to income and then spread among the people. Certainly not in democracy/capitalism.

Follow the consensus among the peer-reviewed empiric evidence.

Also, the value of a model lies in its predictive capability. Look at what side made the most correct predictions.

So, to apply this to your evolution example: The scientific community is peer-reviewed and empiric, thus reliable. New ideas in science will have to stand on their evidence, and if they can be proven inconsistent with evidence, they are struck down. The absoluteness of the speed of light has been one of the most hated and fought-against facts in all of physics, yet it is in our textbooks, because the evidence did not care about how uncomfortable absolute light speed made the physicits. The local priest's interpretation of how stuff was created, might in the best case be peer-reviewed in that it's discussed among priests. but it is not empiric., which gives it little value.
Evolution predicted that we will find more missing links and how they might look. Your priest probably won't make any accurate predictions of the future based on the bible (the world still exists, after all)

This is the whole purpose for establishing a Republic and not a Democracy. By having the people elect elites/experts/professionals they can therefor make those decisions and learn how everything works. Determining who is qualified by disseminating the issues is quite a feat in itself but addressing issues directly as in making law and determining the actual impact directly created from your decision, is quite the undertaking. Elections are fundamentally flawed in this regard, since non experts need to decide who is best and the line that determines the winner is majority vote, causing involved politicians to need to gear their efforts not just to prove qualifications but to convince as many people as they can. In the end, it is trust that the people will choose someone capable and that the majority can't be deceived. In the case they are or something changes we have means to remove elected officials from office. It's a messy mash up of checks and balances that allow our flawed system to work and it has thus been determined to be the best option for government. More educated than Democracy and less abusive than Dictatorship, in exchange for a level of cumbersome.

My understanding was that you're not sure what you can trust and what you can't. Political biases exist everywhere, and they constantly skew data one way or the other. My answer is that if something is logically consistent, it is more likely to be true than something that is not. I hold consistency in such high regard because I do not believe that an arbitrary system can be correct, and I believe that an arbitrary system leads to a far worse society than a consistent one. An arbitrary system can be changed to enforce anything at all, and you can only claim it to be wrong based on yourn personal beliefs. 

You are willing to ignore anything in order to save lives. Let's look at the trolley problem. You're on a runaway train car, and there's no way to stop it. Tied to the tracks are five innocent people. If you do nothing, they will die. There is a switch that will let you move the cart onto a new track. If you do so, however, one person will be killed by the car. By your reasoning, I would assume that you would press the switch and kill one person rather than five. 

My problem with this, is that while you may end up with a lower net loss of life, you have decided that the life of that one person was worth less than the lives of five others. That value is subjective. For the family of that one person, he may have been worth far more than the other five. You have not created a net good, but shifted the hurt to another area. You have also asserted that you can decide who is worth more. What if that one person was on the verge of curing all cancer? Would that have been a net good for the world? Or what if someone else claimed that the life of one was worth more than the lives of five? Who's claim is more correct?

Yes, this scenario is purely hypothetical. But let's look at a more realistic one... Say, a terrorist group attacks the US. The US responds by going to war against said group in the hopes of preventing more US deaths. Along the way, many innocent citizens of the country in which the terrorist group resides are killed. This is explained as an acceptable sacrifice to prevent the deaths of more Americans. Do you claim that to be justified? 

How about this case; The US has constructed a horrible new bomb, the most destructive ever created. It now plans to employ these bombs in order to end the bloodiest conflict in the history of the world, and it prefers doing this as all estimates of a land invasion show a much larger loss of life than should these bombs be used. They end up being used, and the final number of casualties is indeed lower than the estimated cost of life of a land invasion. The effects last for decades after and some innocent people are forced to live with the result for the rest of their lives, but there are fewer overall casualties. Is this justified?

One of the first things that the professor in my cryptography class told us students was that pretty much everything we know or believe is ultimatively based on trust. There's hardly anything that we have actually verified.

There's no definite solution to this dilemma, in the end, you can never know for sure. In the case of opposing models/explanations/theories, I believe the best practical solution is to hear all sides and simply consider what explanation you find most plausible.
In the case of evolution vs. "god created earth 6000 years ago" for example, I believe evolution simply offers a much better model, as it offers a measurable and plausible explanation for many things that you can discover in nature.

I don't want to get too in-depth here, but not all models are judged by their predictive capabilities. Just as a simple example, the fact that a model produces an accurate prediction does not mean that the model itself is supplying an accuarte identification of causal relationships and mechanisms (kind of the traditional problem between causation and correlation). I could create a model that produced accurate predictions based on correlations, but the explanatory power of this model would be incredibly limited.

I was about to type something similar, so I will just second this. The main question is who to trust. The answer is simpler when talking about the hard sciences (trust the scientists, for the most part), but its a bit more complicated when talking about politics or almost any other area of study because there's not much that is readily agreed upon, outside of tautologies or trivial truths.

I came into this thread expecting you to say you had anal sex with a Thai ladyboy and you only found out he was a man the following morning. I am disappoint