This is not entirely accurate, and a bit of a hollow victory to walk away with that conclusion.
It does turns out that "27% of Clinton supporters" think that the US "does not have a responsibility to accept refugees from Syria." But that is not really the point of the study.
The main point of that research is to illustrate that the US has allowed refugees into this nation all along, even though the amounts of those allowed in fluctuate based on "global events" (which of course determines who qualifies as refugee) and political dispositions of our government at the time. The biggest impact to the trend, over the study period, was post 9-11 thinking. When this nation by majority decided "safety at the expense of liberty" and we birthed today's flavor of anti-refugee sentiment that still exists today, created the bloated NSA and all that it implies, designed systematic removal of the 4th Amendment at the whim of political intentions, and in the end came up with the Patriot Act that turned out to be the largest power grab by the government over the populace in modern times. Also important to note, while the influx of Muslim refugees was on the incline before Trump's policies we were still accepting plenty of others from other religions as well. At the same time we have been allowing Muslim refugees into this nation both before and after 9-11 suggesting the politics of the situation is what people are clinging to instead of the facts the Pew Report is trying to present.
All that said, the stat that "54% of registered voters said the U.S. does not have a responsibility to accept refugees from Syria, while 41% said it does" means that 54% of the nation is looking to continued governance to "protect them" via the illusion of policy they think keeps them safe. Those are political leaning determinations, and that is with the harsh reality that we have little evidence we are more really more safe after Trump's policies. And speaking of Trump, all he represents is a shift to right leaning authoritarianism from Obama's brand of left wing authoritarianism.
In the end the conclusion is the same, the illusion of safety.