I wouldn't say refuse access to all refugees, but proper screening definitely needs to be in place, proper processing otherwise you can change that cartoon to feature one of the family members holding a knife or bomb and that will be another alternative way one can view it all, especially as one of the accused in Paris was said to have been rescued as an asylum seeker in an overturned lifeboat
If these people want asylum then they can have it, but only when procedures are followed, and this unfortunately means asylum camps, long waits among other things, but then, who funds these camps? Who enforces law in these places?