Because [liberals are] blinded by the lies and their desires/preferences to believe the lies over the Truth. Many of them may even have Muslim friends, and so through them, they believe that Islam is a peaceful religion, and if Islam is peaceful, then those causing the trouble and killings must be a small group of people ("radicals") among them. But like you said, if they'd just open their eyes to see what's happened to other countries who let in the Muslim refugees from Syria, a country that's known for always being at war with their surrounding nations (even in Old Testament times), and if they'd recognize that Islam isn't a peaceful religion, then they'd see that it really wouldn't be a good idea to let them into here.

When you research about Islam, you see that it's not a peaceful religion, but one based on lies, distrust, and hatred towards people different from them (pure racism, homophobia, sexism, anti-semitism, etc. are all parts of Islam). Even Bill Mahr, a well-known atheist who likes to make fun of Christianity and religions, researched Islam and found the same, and when he came out to warn people about it, other liberals argued with him about it, too. So even when one of their own learns the truth about something, they continue to disregard it.

So why do they continue to reject the Truth? Some are ignorant, some are blind, some, I think, want so badly to promote world peace and their agenda that they fail to see the evidence against them - or they see it and reject it due to their beliefs about people and their impossible agendas for the world.

But Theologically-speaking, the Bible even tells us this would happen. Peter talked about it, Paul talked about it, Jesus talked about it, prophecies from Revelation, Daniel and Ezekiel talk about it...so in a sense, it all has to happen and is set to happen. That's not meant as a cop-out to accept the liberals' ignorance, but a reminded that nothing that's happening should be surprising. Satan lies to liberals and others who will listen to him, using their emotions against their better judgment and blinding them to the Truth. Like you said, they claim to be against everything, yet are (somehow unknowingly) standing for the same thing they say they're against. Maybe it has to happen to them before they finally see, who knows