I didn't read it as they were pushing a religion. I read it as the DoD 'endorsed' the tour of this group, meaning the DoD didn't have a problem with it from a security perspective.
I'm sure the DoD has 'endorsed' (meaning okayed) other tours as well, even those of the leftist Hollyweird types who go over to visit the soldiers.
“I didn’t read it as they were pushing a religion...”
Try reading it more slowly.
“The entertainment includes the distribution of packets with religious tracts...”