The problem is not keeping religion out of politics, never has been, in-fact, that argument is rather stupid. As I'm sure everyone here knows, nowhere in the constitution or the words "The separation of church & state." The only thing mentioned is congress shall establish nor prohibit any religion.
Here's the thing, the problem is when government infiltrates the church in order to pass policy...not when religion is part of government, meaning, when religion is part of a politicians principles, that's fine. If a governing individual rules based on the convictions of his principles, this is proper, when a government official uses the church to influence policy, this is a problem...there is a big difference in-between the two.
And the idea that someone can govern without their principles, which are held by their religion or lack thereof, that idea that a person should or even can withhold his principles is beyond naive and simply stupid.
What Obama is doing here is outright wrong.