Like immigration and abortion libertarians have a different opinions on what the proper response to accepting refugees from Syria are. Before answering we should look at these factors:
The Welfare State
As far as we know, any refugees that are taken in can receive welfare benefits (housing, medical care, public "education" etc). As libertarians we know that the welfare state in it's current form is evil. It's a system build on theft and force with the threat of being locked in a government cage if one refuses to pay into the system. Adding more people to this system will only result in the state forcibly confiscating more of our hard earned labor in order to keep up with the increased burden on it.
Private Property
While nothing has been state on either the mainstream media or alternative media outlets lets not be fooled that with the state importing people that we have a good chance of seeing private property rights being violated. What if lands and public housing project which are designated to house the refugees all of a sudden become full for whatever reason and then the government starts going after people who have large amounts of land such as farmers? As a rule libertarians don't put anything past government and what they may or may not do. It's completely believable that governments would threaten large land owners into accepting refugees on their land. Also not just farmers, people who own apartment complexes and buildings could be told that they have accept refugees at whatever rate that the government thinks is "fair".
Based on these two issues alone any libertarian in good faith can't be for the state importing massive amounts of people at a fast rate. Even if the state says it's being humanitarian we all know that anything that the state does has an underlining purpose from what they say upfront. However it's not to say that libertarians should be against people who wish to sponsor refugees with their own resources. That's perfectly within libertarian philosophy and should be encouraged instead of a massive all at once importation. It actually somewhat surprises me that even the MSM isn't even suggesting that this is even an option.
Some may be reading this and say that this is no different than what conservatives are saying. I would say Yes but it's not just against the massive importation that libertarians should be against. In addition to this we as a movement should be highlighting on our blogs, podcasts, YouTube videos that this crisis is the result of years of meddling in the Middle East. It should be highlighted that once again Ron Paul was right. As horrible as it sounds, Iraq, Syria and Libya were much more stable when Saddam, Gaddafi and Assad were in charge. Yes all three of these countries were socialist hell holes but the religious and ethnic strife wasn't there as all three leaders stressed nationalism over religion and ethnicity and believe it or not Islamists weren't tolerated in those countries. When Islamists attempt to set up shop they were regularly jailed and executed. With them gone the fringe hate groups took over the country with the regular people fled or got killed. Conservatives don't want to acknowledge this, there solution is just to continue to bomb these countries like the government has been doing since 2003. The warfare state created the instability but it's not going to fix it, only make it worse.
