>”Isn’t it possible that [others] … have opinions and belief systems just as valid as yours?”
I think it’s fundamentally impossible for people to grant that other people’s belief systems are equally valid. Our belief systems are how we understand the world; they are, in effect, our reality. A clear example surely is religious belief — if I am profoundly convinced that a specific deity created the world and runs it today, I can’t really grant that well, maybe it’s really your deity that does that. (Religion is just one example here.)
The best we can hope for, I think, is tolerance — that while your religious belief (or whatever worldview you have) is clearly wrong (mine is the truth, duh, else I wouldn’t believe it), I can grant that you’re allowed in our society not only to believe your beliefs, but state them, proselytize them, whatever . Just like I am. And that I must respect that.