They know nukes are radioactive, right?
When the Nazis were planning their big attack, the guy in charge was wildly rattling off names of cities to be hit with nuclear bombs and the others were happy about it.
He even goes back and adds Tokyo when he realizes that it had been left off the list even though the Japanese home islands alone were already targeted in about ten other places. Himmler of all people is the only one who seems concerned.
I'd expect them not to care about the massive loss of human life, but since they hate birth defects and incurable illnesses so much, I thought someone would object. It's not like they're planning to stay out of the effected areas, either. Their sending the army right in--young men whom they would want fathering more children.