They could have fled for any number of reasons- that doesn't mean that they aren't exactly in sync with the culture they are coming from. And even if they aren't in sync with the culture they are fleeing- they very likely still hold radically different values than you.

I met a man from Afghanistan sometime last year, however, once we got past the introductions and realized we shared things in common- he opened up to me and began trying to make me realize the value of Sharia law in America, and how much better it would be here if it became the cultural norm.

I’ve had that experience as well, except instead of Afghanistan it was America, and instead of Sharia law it was Biblical law.

I am far more afraid of certain of my native-born countrymen than I am of people who come here.

Sharia law is quite big! So big that I'm fairly certain that there is at least one aspect of Sharia law that you would agree with, even if (as it sounds like) you are overall against. If you accept that, you can have a honest discussion of the merits and detriments.

I find it's best to break these things down and discuss them individually (or discuss how multiple rules combine to produce a particular effect, as the case may be): then it's easier to tease out which arguments are honest ("I genuinely think X is better, for Y reasons") and dishonest ("I think X is better for Y reasons, but I believe you'll find Z more persuasive, so I'll say Z"). There's also a phenomenon where people attribute beneficial (or detrimental) properties to one, visible part of a system, when they're really due to another: consider the arguments about capitalism versus communism, which are rarely actually about economic policy, and are more often about other (on the face of it, unrelated) policies of the state: your interlocutor might realise this after detailed discussion, if that is what is going on, when otherwise they might have gone their whole life without noticing the misattribution (as many people do).

Cultural exchange can be mutually-beneficial, even if you both go away thinking "wow, that other guy was an idiot".