O'Keefe praised the omission of both policies.
"Being a Syrian doesn't predispose one to any of the things that our vetting system would look out for," he said of there being no indefinite ban on Syrian refugee resettlement.
Also, religious-based persecution is already one of five criteria of vulnerability for those refugees who are being vetted for admission to the U.S., he noted, adding that some "local church leaders" have said that a special designation "wouldn't be helpful" and "actually exposes them to greater danger."
However, some have been pushing for a special refugee status for persecuted religious minorities, especially those in Syria.
Persecuted Christian minorities, including genocide victims, must have a "fair outcome" when looking to resettle elsewhere, Andrew Walther, vice president of communications and strategic planning at the Knights of Columbus, explained to CNA.
"As part of the review of the refugee admissions procedure, the UNHCR referral process for refugees should be closely scrutinized, and the serious inequities in the number of Syrian refugees admitted from communities targeted for genocide should be rectified," he said. Refugees must first register with the UNHCR to be eligible for resettlement.
Yet although Christians make up only a small percentage of the Syrian population, the percentage of Christian refugees from Syria who are resettled in the U.S. is even smaller, Walther noted.
"The Obama administration policy was to prioritize these groups, but despite this they remain severely underrepresented in U.S. refugee admissions, so it's clear that a fair outcome is even more important than a stated priority," he said.
Syriac Patriarch Ignatius Joseph III Younan of Antioch has warned that Christians hoping to be resettled in the U.S. or Canada have never even had the chance.
"I personally heard on several occasions from many of our Christian refugees in Lebanon and Jordan, that their applications for refugee visas, either to the USA or Canada, are without any response, if not refused by the consulates of the USA and Canada," he stated.
Elsewhere in the executive order, a ban on entry by most foreign nationals into the U.S. from six countries is still in effect. The countries are Iran, Syria, Yemen, Libya, Somalia, and Sudan, while Iraq, which was formerly on the list, is now omitted.
(Story continues below)
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Exceptions to the visa ban include refugees already admitted to the U.S., lawful permanent residents, those who received visas before 5 p.m. ET on Jan. 27 – the date of the original executive order – and those travelling on diplomatic visas.
Yemen and Somalia have "developing famines" and their own conflicts, so "it strikes us as cruel, actually, to restrict the number of people who can come," O'Keefe said.
Catholic Charities, USA, whose affiliates partner with the government to help resettle refugees in the U.S., spoke out strongly against the temporary refugee ban.
"At the heart of the work of Catholic Charities is the Gospel mandate to welcome the stranger and care for the most vulnerable among us," Sister Donna Markham O.P., president of Catholic Charities, USA, stated on Monday.
"Today's executive order not only hinders that work, but also effectively abandons, for four months, the thousands of endangered refugees fleeing violence, starvation and persecution," she said.
The group "is leading an ambitious $8 million campaign to support the work of local Catholic Charities agencies in caring for refugees."