Is it OK to allow people into our country who hate it and want to undermine it?

Just asking. I keep hearing that keeping out any sort of immigrant is anti-American values? So where should we draw the line on who should be let in and who should not be?

If there is a line to be drawn, then shouldn't we do a better job of protecting our borders, since someone who hates America and wants to attack it from within would certainly try to come into the country the same way millions of people have successfully immigrated before, right?