Has Donald Trump indicated how he want refugees who are neither Muslim or Christian to be treated? For example, has he mentioned how Yazidis should be treated?
Failing that, has any prominent political figure, advocating differential treatment based on religious affiliation (including atheism), mentioned how Syrian refugees who are neither their own religious affiliation nor Muslim should be treated?
We can pierce it together by joining several statements. First there is a part of the Executive Order known as the (first) travel ban that says:
(b) Upon the resumption of USRAP admissions, the Secretary of State, in consultation with the Secretary of Homeland Security, is further directed to make changes, to the extent permitted by law, to prioritize refugee claims made by individuals on the basis of religious-based persecution, provided that the religion of the individual is a minority religion in the individual's country of nationality. Where necessary and appropriate, the Secretaries of State and Homeland Security shall recommend legislation to the President that would assist with such prioritization1.(emphasis mine)
So Trump is willing to prioritize religious minority of any kind. Although before that, the orders says that it would block all people from specific countries. So he isn't willing to absolutely prioritize religious minority over any other consideration. If refugees can come, then religious minorities are prioritized, otherwise they don't get special treament.
On the other hand he has also said that he would prioritize especially Christian refugees. Although he said that in an interview to a Christian media and not in an official policy.
Another important fact is that he said, during the electoral campaign that it's difficult for Christians refugees to prove that they actually are Christians. It's fair to assume that this also applies to other religious minorities. This would explain why he didn't exclude minorities from the temporary ban, but it could also make difficult to prioritize religious minorities in the future.
Shortly before issuing a sweeping executive order to suspend refugee admissions for 120 days, President Trump gave an interview in which he said he wanted to give priority to Christians in Syria. (The actual order does not single out Christians, but religious minorities in countries.) He said that “if you were a Christian in Syria it was impossible, at least very tough to get into the United States.”
