In this instance I was not discussing ID, but YEC, using it as an example. YEC makes specific testable predictions that can be scientifically proven to be false. Even though YEC is a religious idea, the science that contradicts YEC is not religious.
Dembski and his allies have tried to have it both ways about the religious content of ID. In some contexts, they've heralded it as completely secular - the designer is not specified. In other circumstances, they've made triumphalist statements about how it's a clever way to get religion taught in the science classroom. Dembski has even tried to claim that while ID is not religious (contradicting himself) any attempt to disprove it is religious. If you've been following the testimony in the Dover trial, the plaintiffs have been able, over the strenuous efforts of the defense, to get statements about the 'wedge strategy' into the court record.
I can't speak for his "allies", but Dembski did not, in the statements you quoted, herald ID as a way of getting religion taught in the science classroom.