I accept the science of evolution, and I believe that species give rise to new species through natural selection. If a squirrel is found in the same rock layer as a trilobite, then guess what? It's wrong.
I accept the idea that cars require gasoline in order for them to run. If my wife starts putting apple juice in the tank and gets around town just fine, then guess what? It's wrong.
Everything that I accept about the world is subject to being wrong as far as I'm concerned. There are plenty of things where I don't really give it too much likelihood that it will be proven wrong, but I have enough humility to know that my perceptions can be completely off when it comes to discerning what's true and what isn't. I try my best to determine when it comes things where I have a strong opinion (evolution, climate change, etc.) as to exactly what it is that would make me admit that I'm wrong.
Contrast this with some things which I regard to NOT be true and some of the common attitudes you'll find.
There are people who believe that praying to a deity will bring about a miracle, whether it's being cured from an illness or getting out of some financial difficulty. When the prayer doesn't result in the desired result, do they say that the prayer "didn't work"? That's not my experience. Instead, they backtrack and give excuses. They'll say something along the lines of (and I'm quoting from a Facebook post here) "It (the miracle) just might not happen the way he expected it would." Another response goes along the lines of: "IMO, praises and prayers dont fail, sometimes its manifestations may be delayed or prolly you dont have enough faith" (sic).
You can check out an entire page that addresses why God doesn't answer prayers. The reasons include that maybe YOU don't have enough faith (which makes it your fault, ya know), sin, and he's going to get around to it eventually. Nowhere is the most obvious answer, the one that requires the least amount of assumptions, addressed.
In other words, to people like this, there is no way that they can be wrong. When it works, it works. When it doesn't work, it still works. What would convince me that it works? If it worked at a statistical rate that was better than chance. Until then, these explanations appear to me to be nothing more than cop-outs.
A similar situation is with astrology. When a person matches up with the description of his or her astrological sign, then that's proof that it's working. When they don't, well, you have to look at what stars and planets were ascending at the time of the person's birth. Or you have to look at exactly what day and year the person was born. In other words, if it works, it works; if it doesn't work, then you can still get it to work. From what I know, astrology has no criteria that would successfully debunk it for its adherents. (Which is why it split off from an actual science, astronomy, long ago.)
What would make me believe it? If astrologers could give accurate and specific readings based on whatever information they think that they need. From my understanding, every time it's been put to the test, they have failed miserably, as their descriptions are either spectacularly off or too vague to determine its veracity. See the video below to see how these things go. (And it should be noted that a million dollars is waiting for any of them who can successfully demonstrate their claims in controlled conditions. When somebody collects, I'll change my mind.)
I think that the important question, no matter what issue we're talking about, is to ask yourself whether you care or not whether your beliefs are true. If you don't care, well then, you can just ignore all of this. If you do care, then you have to not only be open to changing your mind, but you have to know exactly what WOULD change your mind.