I am more concerned with the lack of assimilation that these refugee groups pose to us as a culture and society of laws. Specifically the desire to form enclaves separate with sharia laws and maintain their own social order and customs separate doesn't bode well for our melting pot society.
While I think that is a legitimate worry I don't think it is much of a problem here, especially when it comes to refugees from the Middle East. Why? There simply aren't the numbers and concentrations here. There are concentrations of certain groups in certain parts of the country; Iranians in LA, Kurds in Memphis, Somalis in Minneapolis and Arabs in Michigan, but they are merely drops in the bucket compared to the population of this country and the other groups of immigrants here that far outnumber them. It is a bit different in some parts of Europe where there are much more higher percentages from particular countries or regions like Northern Africans in France or Turks in Germany.
The biggest difference though is that we are a nation of immigrants that has been assimilating immigrants for over 400 years, and there is no ethnic group that is 'American' like there is in Europe. This results in a completely different attitude towards what qualifies one as an 'American' here than other countries where ethnicity plays a role. It is that attitude that has allowed the son of a Kenyan become our President and bunch of children of immigrants be viable contenders to be his successor.
I worked closely with some Americans who had immigrated from the Middle East, Arab and Kurd, and found them to be pretty well assimilated after an average of 20 or so years in the country. Many had come to the US as refugees in the wake of Desert Storm and as a group had done pretty well. What was most striking was that their children not only had assimilated but from what I saw were mostly indistinguishable from an 'average' American kids even in appearance.
On an even more personal level, the experience with bringing my wife into the country was pretty eye-opening as to how extensive and thorough the process was just for a regular visa just for a Canadian. The refugee process is much more extensive.
Paris has even allowed the establishment of sharia courts in their country and basically has Muslim enclaves where they pursue their culture apart from the host nation. That for me is a recipe for failure. I don't have the link handy but earlier this decade the Australian PM told immigrants that they needed to adopt the culture and life of being an Australian or leave. Why can't we do the same and have them speak our language, respect our laws, enfranchise their women and children. Etc. Sadly I think the beliefs and attitudes of this group of immigrants (using a very broad brush) is inimical and counter to our culture and laws.
Do you realize we have religious 'courts' in this country? Both Christian and Jewish. They are really more arbitration panels that handle civil matters with the consent of all parties and can't clash with established law, they also don't touch criminal law in any way. 'Sharia courts' in France fall under this category and can't conflict with the government law there.
And I personally don't think we as Americans need to be the solution for all the worlds problems and tragedies.
Neither do I but as the world's richest country, one that has not only helped keep the world a little bit safer but benefited from it as well, I think we are obligated to do our part.