You guys are seeing contradictions that do not exist.
This country’s society for the last forty years has been dominated by liberalism.
This does not mean that the government enforces liberalism.
And it does not mean that ideologies contrary to liberalism have no power.
Thus, a society of the future might be predominately secular and atheistic, but still vulnerable to agitation from other quarters…such as Islam.
Gingrich’s concerns are two-fold: One, that the U.S. in a generation or two will be dominated socially by liberals (hence secularism and atheism); and two, given that liberals are almost always willing to bend over and take it up the butt in order to claim the moral high ground, they will allow aggressive, radical Islam to overtake society rather than stand up to it and be perceived as “racists”.
So he’s predicting a progression in which America, having become secular and atheistic (i.e., liberal), will begin to be overrun by Islam because of a liberal lack of will to resist it.
Now, we can debate whether that will ever happen (and for the record, Gingrich’s beliefs are not necessarily my own), but it’s not accurate to try to portray Gingrich’s comments as saying that in the future we will be governed by atheists, except that at the same time we will be governed by Muslims.
So again it’s a “progression”, rather than conflicting ideologies predominating at the same time.