The Baptist Joint Committee's Brent Walker discusses the question of religious displays at the White House.
The White House is different. Yes, the federal government owns it, and in a sense, it is "the peoples' house." But not really. It's predominantly the residence of the government's tenant – the President and his family. I don't have free and unfettered access to the residence; I (unlike the Salahis) can come only by invitation of the family who lives there.
So, in this context, the crèche in the East Room is more like an individual displaying it in a private home or on one's lawn or a church doing so in the church yard.