This is a very interesting question to me.
The scriptures say seek knowledge by learning and by faith. So the Lord wants us to use our brains and to learn. But he also wants us to develop faith.
When you do become educated, you learn that science is the major competing worldview to religion. At their core, science and religion are both talking about truth, but we don't know enough to see how they are connected a lot of the time.
Science is a very specific method - it can only talk about what you can measure. If you can't measure it, science can't touch it. Also, science is always tentative. It never has final answers.
I love learning about science. I think it is a very valuable tool for discovering truth. However, some people make it into more than a tool, and start to treat it like a religion, making it into a complete worldview. The problem with this is that science is limited and is always changing it's theories.
Religion is a very different way to truth. It is all about revelation from God. And also faith is required - the first principle of our LDS religion, in fact. Faith to me means trusting God. As we are obedient to God, our faith will increase.
I think it is possible in this life to get along fine without learning science or the "internet controversies." The most important thing is learning to love God and love your neighbor. But my personality is to ask questions, and I think God likes us to learn.
It is extremely foolish to decide whether the church is true based on things like "no evidence has been found for horses in the Americas." Let's use this as an example: First of all, lack of evidence doesn't prove anything. It just means so far we haven't found anything. Also, the Americas - that's a huge area. We don't know where the Book of Mormon people lived. Much of the Americas is not dry arid desert, where stuff would just lie on the ground, uncovered, and preserved by dryness. Also, how hard have archaeologists looked for horse bones? Say you find some bones, and you already "know" they can't be horse bones. Are you going to pay a lot of money to have them tested? Bias like this can influence what has been "found."
I have looked into most of the "internet controversies" and found reasonable explanations for things. Sometimes you have to take things on faith while you keep learning - suspend judgement. And sometimes you must take things on faith all your life. Luckily, we have the Holy Spirit - when you feel that, that is evidence that speaks to your soul.
Two great sources for answers to the "internet controversies" are the Gospel Topics essays on LDS.org, and the Fairmormon.org apologists site.
https://www.lds.org/topics/essays
http://en.fairmormon.org/Table_of_Contents