There are some issues where a) I have no direct knowledge of the facts, b) there is some dispute over the facts, c) I hold an opinion on what the facts are. You probably do too.
For example, I believe that ~6mm Jews were killed in WWII, and that most people who deny this are anti-semites. If someone produced a theory which conflicted with my views, I would probably be very suspicious of the person's motives. I think this without ever having seen evidence that would satisfy me directly. [I've been to Auschwitz and a few other camps, and I've read a few books about WWII, but the only reason I have to cite the figure of 6mm rather than 3mm, or even 300,000, is that most knowledgeable people use that number]. I suspect most LWers are at a similar state of opinionated ignorance.
Now, I am in no way incentivised to investigate this: my opinions matter roughly zero to anyone, including me. So I don't have any reason to investigate the Holocaust. But there are other areas where the facts do matter to me.
I know very little about medicine. When I need medical assistance, I tend to do what a doctor tells me without criticising his diagnosis. For example, I suffered from eczema a few years ago. I was prescribed a medicine which contained hydrocortisone as the active ingredient. I Googled this ingredient and then took the medication until the affected area cleared up. I noted that there were other steroids available [Clobetasol propionate is one such] which are considered cures for eczema. I did not know why my doctor prescribed me one rather than the other, and the distinction between the two would likely affect me. But I took the 'expert advice' without a pinch of salt. Unlike the WWII question, here the facts are actually relevant to me, and a mis-diagnosis could have caused some complications. But just as I don't check the wiring of my house's electric systems, or check my walls' stability and capacity to support my ceiling, I take my doctor's advice.
There are some less clear-cut examples. For example, the 'smartest' [read: some combination of high-IQ, high-rationality, knowledgeable] people I know tend to identify as either libertarians or utilitarians, rather than as socialists. There are a few exceptions to this, but not many. From this, I could arguably assume that it would be correct to adopt a libertarian or utilitarian, rather than a socialist*, mindset to politics without actually understanding why libertarians are libertarian. Just as I don't need to know why my doctor prescribed hydrocortisone in order to take it, I don't need to know why most smart people I know favour relaxed drug laws in order to share their opinion.
*I'm aware that these are not the only options, but they're the most mainstream 'labels' which are clearly defined. ['Liberal' and 'conservative' mean different things in different countries, but I think those three are relatively constant, at least in the people who apply them to themselves]