This x100. The worst case scenario is to let them in, but treat them like they are all terrorist suspects who don't fit it in.
Fundamentally, Europeans have had a different attitude about race and ethnicity than Americans do. Almost everybody in the US traces their history back to an immigrant who assimilated in some way. Accordingly, the American identity hasn't centered along race and ethnicity to the same extent, so we're quicker to assimilate ethnic Irishmen, French, Germans, Poles, etc. For example, my ancestry is English, Welsh, and Italian, but I have an American cultural identity. I speak English because it's the native language of the US, but I know no Welsh colloquialisms and speak no Italian. Even my grandmother whose parents emigrated from Italy knew very little Italian, had no Italian accent, and never spoke Italian at home. I think that's true for the overwhelming majority of US citizens. Obviously, the more an immigrant looks, talks, and lives differently than the majority, the tougher it is, but I think the tendency still leans toward assimilation.
In Europe, that's not how it works. A Pole living in Britain is a Pole, not a Brit, even if he speaks English and is a British citizen. His neighbors see him as a Pole, and he thinks of himself as a Pole. This is why Germans were expelled from Eastern Europe after World War II. Before the War, there were millions of Germans living in Poland and Czechoslovakia, whom Hitler referred to as "Volksdeutsche" ("racially German"). Even though they were Polish and Czechoslovakian citizens and often had longstanding roots in those countries, they identified as Germans, spoke German at home, associated with other Germans, were loyal to Germany, and collaborated with the Nazis to help destroy their nations of citizenship.
I think a similar attitude took place with Muslim immigrants to Europe. The Muslims who live here don't identify as Germans or French. They identify as Turks, Algerians, etc. and most of all, as Muslims. Furthermore, the native population also sees them that way, so they don't see assimilating them as French or Germans as being much of a priority or even necessarily possible. I think that coupled with social media makes it much easier to radicalize them. If an ethnic Algerian goes and shoots up a nightclub in Paris, he's not killing his own countrymen. He's killing an enemy that's foreign to him and treats him as such.
This is where the multiculturalism "salad bowl" horse crap gets dangerous. When we're talking about ethnic Mexicans who don't have an ideological hostility to the West, it's not as big of a deal. There isn't a serious effort by Mexicans to reconquer parts of the United States and kill its people. But when we're talking about people who do have such an ideological hostility and can be easily be reached by organized outside groups like ISIS who can encourage and pay them to commit acts of terror, multiculturalism can get deadly in a hurry.