The United States is a Christian nation with separation of church and state, which means that the government doesn't dictate how the church is run. Churches have the right to operate free from governmental interference, and what that really means, is that the people have the freedom to live their lives in worship and obedience to God without the government passing laws that would oppose. In fact, the government is to protect the right of the people to live, work and speak as they believe.
The church is the ecclesia, or governing body of the Lord in the earth. The constitution was written to protect the church and the freedom of the people to worship freely. People are allowed to worship freely in their homes, their churches, and in the "public square" and business. These freedoms were given to the church at its founding. It was presumed that we would always remain a Christian nation.
So what do we do when an ideology which opposes both the church and the constitution, calls itself a religion and tries to claim the same freedom that the constitution provides to the church? Our government should recognize that these attempts are direct attacks on our freedom and oppose them. It should not open its arms to "religions" who oppose the constitution, such as Islam's Sharia law. Their goal is to remove and replace the church in America, not simply get in on the freedom of worship, and they will do that by force if it comes to the point where they feel they could.
As the ecclesia in America, the responsibility of the American church (or American Christians) is to prohibit anything that opposes this freedom from infiltrating or gaining a foothold in our land. Some of this is done spiritually in prayer and proclamation, yet as Americans who have both the right and responsibility to vote and hold our legislatures accountable, we are to take action through "non-spiritual" means as well.
In the Old Testament, we see that God's people got into trouble whenever they wouldn't tear down "the high places" or when they would allow those who worshiped false gods to remain in the land after He told them to go in and possess it. In the same way, if we allow those who oppose the Lord to promote their ways, and increase in both number and influence, then we are removing the protection and blessing that He has placed over us. Our own actions (or inaction) will be the very thing that becomes a snare and takes us down.
Compromise is not the answer. Political correctness is not the answer. This isn't even about immigration or refugees. It's about protecting the Judaeo Christian values that we were founded on, and not being so naive as to think that we are somehow immune from having enemies who hate us, just because we're "nice." Do we love our enemies as Jesus said? Absolutely, but we love God more, and work to build His kingdom, defend the faith, and the land He's entrusted to us.