I have not seen any credible evidence that the Obama administration is favoring one religious group at the expense of another. After reading this thread, I still haven't.
As for President Obama's claim that we do not have a religious litmus test for refugees in this country, it is my understanding that the new reality (in which this is indeed the case) is the result of changes to the immigration system in the 1960s, and that before that time the religion of people coming into this country was at least taken into consideration with regard to their ability to adjust to a society made up primarily of Christians and Jews. Some would say that this would not be a bad thing to return to, and I would agree insofar as I think that pretending that religious difference doesn't matter just because we'd like it not to is a bit like people who claim not to see skin color or what have you. Okay, sure, you try to treat everyone equally, but usually the people you're trying to impress by saying that sort of thing are already well aware of their skin color and the impact it has on their daily lives as minorities in this country. So I can't help but say that it strikes me as at best disingenuous. I probably like President Obama more than most people on this board, but I must admit it does bother me that he (and with him, seemingly large numbers of secular society) seems to treat religion as an afterthought or non-issue when the people he's actually talking about don't. I remember some years ago when the author Salman Rushdie (who I would think knows a thing or two about the threat posed by Islamic extremism) was asked by Bill Moyers of PBS in the latter's "Faith and Reason" interview series whether or not he ever had trouble writing about religion or religious people, since Rushdie himself is an atheist. Rushdie's brilliantly simple reply was something like "Well, no, not really; it doesn't matter if I'm a believer, since all the people I'm writing about are."
It seems to me that large numbers of the current political elite and even ordinary citizenry cannot see the wisdom in this kind of approach, and in enforcing through various means their secularist worldview, are setting all of us up for great harm in the future via the inevitable clash between those who are really, really committed to extremist versions of their religions (Islam and others), and those who cannot even countenance that this could ever be the case because after all religion is a private matter, not relevant to public policy because we're not a theocracy, irrelevant and for old people anyway, or any of the other things I'm sure we've all regularly heard in several iterations for quite a long time now.
The propagation of this secularist worldview (even or perhaps especially by self-identified Christians like President Obama) means that we are in fact, as a society, thoroughly unequipped to deal with the reality of religion-based terrorism (and Islam-based terrorism in particular, given how we don't understand Islamic societies like we think we understand or at least can contain Christianity and Judaism, which historically as religions are far more amenable to life under governments that do not defer to their religious sensibilities than Islam has ever been; e.g., in the Coptic liturgy of St. Basil we have prayers for the ruler of the land, without specifying that they are to be Christian, since the liturgy was authored at a time when Christians were not governing any country). It is interesting, because for me as a member of a native Middle Eastern church, I interact regularly with people who have felt the sharp edge of Islam and Islamicization for 14 centuries and counting now, and if an ignorant Westerner who did not have such a background were to place their overall views on Islam and Muslims on a graph, they'd probably be seen as somewhere to the right of Cruz or even Trump. But the idea that this is not a matter of a (only US-relevant) left/right dichotomy is lost on people who cannot see things in religious terms, and instead place their political beliefs (in the absolute equality of all religions, societies, etc.) at the center of how they are going to deal with what are essentially religion-rooted problems (again, according to the people actually fighting and propagating this ideology; it's not as though they don't understand why they themselves are doing these things even as they're telling us and their own recruits that it is all about religious war between Muslims and non-Muslims...give terrorists a little more credit than that! They're dangerous, not stupid).