I think one would be hard-pressed to find anyone who would say "please let dangerous people in". There is a system in place to address that, but no doubt could be improved.
And for those who had family arrive much earlier (such as myself), the criteria for entry was incredibly lax. My mother's side came in the early 1900's so was subject to the 1906 Naturalization Act which basically said "you have to speak english and tell us about family members". My father's side was here early enough to basically just be here long enough and then it's a done deal.
As the OP states, these pogroms are rooted in racism and otherism, and the cruelty is the point. We can do better than that.