It is actually pretty true that Syrian Christians and other religious minorities haven’t been getting into the US as refugees. Out of more than 10,000 Syrian refugees admitted under the Obama administration, fewer than 100 were Christians. Same with Yazidis. Even though both groups have been targeted for genocide by the rebels.
This problem has to do with threatened groups staying away from the UN controlled refugee camps which are overwhelmingly inhabited by Sunnis.
In the Chaldean Christians cited in the article, it looks like ICE has gone after people who have committed crimes or had active removal orders — that they are Chaldean Christians is incidental.
Hopefully, they will be allowed to stay. One of the side effects of the US invasion of Iraq has been the ethnic cleansing of Iraqi Christians.