I am seeing an outpouring of sympathy for the Syrian people who are seeking asylum in the United States.
Some good Christians are of the opinion that we should be willing to open the border and allow them into the country to find safety from all that ails their country.
Other good Christians believe that opening the border to the influx is a dangerous move and we should consider the ramifications of such an act.
I tend to hold to the opinion of the latter. I realize that some will not agree and say that this position is unChristlike and lacking compassion.
The arguments I have heard include the following:
“There are women and children who are seeking to flee to safety. How can we not accept them in?”
I would ask you, did Jesus heal every sick person He encountered? Did He raise every deceased child and bring him back to life? Did every leper get cleansed who came to hear Him preach? Since the answer to these questions is no, was Jesus lacking in compassion?
“Christianity is a religion that teaches us to turn the other cheek and forgive our enemies. Therefore, we should accept these people in although most of them hold an antagonistic if not downright hateful attitude toward western life and the United States.”
Does turning the other cheek mean inviting personal harm into your life? Does forgiving enemies mean opening your borders without a proper vetting procedure in place risking the security of your citizenry? Did Jesus not say that those who would not receive you should be abandoned and the dust shaken from your feet? Why did Jesus tell His disciples to sell their cloak and buy a sword? To pit olives? Why did He say that the thief would have to overcome the strongman of the house before he could spoil the goods if we are not to defend ourselves?
“Bringing the Syrians here would give us an opportunity to be a witness for Christ.”
How many middle easterners/muslims are you currently involved in evangelizing? Would you be willing to surrender to be a missionary to the middle east and preach the gospel of Christ? If not you, maybe send your children? Would you at least make a trip to Dearborn or Hamtramck, Michigan and begin to preach the gospel to the largest group of muslims currently in the U.S.? How about just tell your neighbor about Jesus?
Methinks the compassion crowd needs to involve themselves more in some compassionate acts than social media politics.
Joel Stiff's Adventure 
I’m not exactly sure where I stand on this particular issue, probably somewhere in the middle I suppose. But I do see a few holes in what you have proposed.
Looking at Christ as our great example, his compassion was shown on the cross by giving his life for all. We could live a thousand lifetimes and never come close to showing the compassion he had for the world, so I dont think we should pick and choose whom to show compassion to.
Again, looking at Christ, he not only accepted Judas into his life, but made him one of his chosen twelve. Knowing that he would lead to his personal harm and death, all that his Fathers name would be glorified. If opening up to refugees makes God’s name glorified, then our personal harm would be to His glory.
Some are called to serve in middle eastern countries, some are called to serve in the local churches God has placed them. To presume that someone who is ok with opening the borders isn’t willing to do any of those things you mentioned is very bold. We are called to bloom where we are planted and show Christ to all people.
I may have missed the general point of what you were shooting for, but when I understand the compassion shown to me, I want to do my best to show as much compassion as I can.