Has the word “Birtherism” gotten the currency or ‘citizenship’ as the received English?

Solution 1:

The -ism suffix can indicate a philosophy, belief system, or ideological movement, as in liberalism, Prebyterianism, or Gaullism. Here, it has been affixed to birther, because that is what these conspiracists have become known as, not "birthplaceists" or "originauts" or "Indonizers" or whatnot:

http://oxforddictionaries.com/definition/birther?region=us&q=birther

a person who doubts the legitimacy of Barack Obama’s presidency because of a conspiracy theory that Obama is not a natural-born US citizen [and thus constitutionally ineligible].

As it refers to a specific political movement and not a general concept, and as it is a rather recent phenomenon, I would not expect it to have made its way into too many authorities.

The -er+ism form recalls a slightly older, comparably reputable movement: trutherism, derived from truther.

http://oxforddictionaries.com/definition/truther?region=us&q=truther

a person who doubts the popular account of the terrorist attacks of September 11, 2001, and instead claims complicity on the part of the US government.

I venture to say both words would be familiar to an average reader of the Washington Post, but not necessarily to the average American— any more than Dominionism, Straussianism, or Thatcherism, for example.