DY, according to what I read the vetting process is very extensive. Moreover, if America will go that way it will also have to ban all Moslem students and tourists (don’t forget, tourists sometimes overstay their visas). This would be blatantly unconstitutional. Regarding the attitude towards Jewish refugees (and immigrants in general) there were, in fact, not a few revolutionaries among them. Trotsky, in fact, lived in the Bronx for a number of years after fleeing the Czarist authorities. Emma Goldman also comes to mind. There were also Sacco and Vanzetti.
However, just as there were home-grown radicals (e.g. the IWW or “Wobblies”) then there are home-grown terrorists now. Some of the worst, do not come from Moslem backgrounds at all but have embraced an extremist world-view for personal psychological reasons (the Guardian has an article about this phenomenon along with a caveat). Western countries must be vigilant and use all of the intelligence means available to them but not repeat the tragic mistake of WW2 when Japanese-Americans were interned even though not one had been suspected as an individual of plotting an actual crime (interestingly, the only government official who opposed their internment was J. Edgar Hoover).
BTW, on this general subject there is a book called “Not Fit for Our Society: Immigration and Nativism in America”, which discusses non-welcomes that were given to huddled masses. Benjamin Franklin, for example, warned about German immigrants writing “Why should Pennsylvania, founded by the English, become a Colony of Aliens, who will shortly be so numerous as to Germanize us instead of our Anglifying them, and will never adopt our Language or Customs, any more than they can acquire our Complexion.”