Well nuking the moon and contaminating it is fairly silly, a surface blast would spread the shit everywhere and even a multi-megaton nuke wouldn't leave significant amounts over that sort of surface area, especially considering it's a radiation-blasted hellhole anyway. The issue is the contamination doesn't go away, and would be spread everywhere, because that whole lack of wind and rain means the fallout dust stays on the surface for more or less it's whole half-life anyway.

Now as to 'glassing' Mars, I don't know that I'd want to start terraforming a place by irradiating the hell out of it but Mars is entirely capable of keeping it's oxygen. Atmosphere retention has to do with the V-RMS of the particles in question, relative to the escape velocity of the planet, which from a practical standpoint has to do with how hot the planet gets and what the surface escape velocity is. Earth can't retain molecular hydrogen or helium for that reason, Earth out at Mar's orbit would retain them better because it would be cooler. Mars' escape velocity is 5 km/s vs our own 11, but keep in mind the V-rms is √(3RT/M), essentially oxygen, 16 times heavier than hydrogen, (mono or diatomic) has 1/4th the speed, V-rms, at the same temp, and Temp is fairly minimal as a factor here, as the square root of temps in Kelvin doesn't change much between Earth and Mars. It would leak oxygen and hydrogen faster than Earth - especially from the lack of decent magnetic field - but still ought to be geological timelines not years or decades.

Keep in mind there's precious little practical difference between nuking the fuck out of Mars and bombarding it with icy asteroids and radioactive leftovers are a smaller issue with H-bombs, especially really big ones, because the byproducts of the Fusion stage are very, very short half-life stuff and you just have the radioactive remains of the fission stage which is more or less the same as an A-bomb with a tiny fraction of the power. When you're setting off 100-MT bombs you're getting parallel radioactive debris to a 100-kT in terms of leftover heavier-than-iron stuff because they have around the same amount (kinda). Lighter-than-iron byproducts are usually just temporarily charged, like particles in a radiation suit, don't hold it very long.



American Physicists, last I checked, had a higher rate of military service then any other field except 'military science', followed by engineering, those two would essentially have been the two groups of scientists consulted on the matter. Not a bloodthirsty crowd but contrary to the stereotype weaponization of a given interesting new bit of science is usually very obvious to the discoverers and as a group I'd deem them neither more nor less likely than Random Joe to think that a good or bad thing. The group is further biased since the people asked would have been those from the group disproportionately made up of service members, prior serivce, or those that cheerfully worked with the military all the time, insofar as NASA was more or less a wing of the military back then.

Not caring about the risks though is absurd, that's an engineering issue of ensuring the bomb on rocket or flat out missile didn't disintegrate Challenger-style on the way up through the atmosphere, that wouldn't have bugged them in the planning stage as they'd simply assume they wouldn't shoot the fucker until it was very unlikely to not get there. As a rule scientists aren't noted for saying 'Let's scrap this plan entirely just in case we can't figure out a way to minimize the odds of the rocket exploding, especially since it's just a couple hundred kilos of Uranium or Plutonium raining down not an actual nuke, and we could launch it like we usually do so that the stuff would fall harmlessly into the ocean if it did blow up'.

So the generals were just worried -assuming the article is accurate - because they didn't know better, and are human, whereas the scientists did. Keep in mind that the super-majority of people who do the science and engineering on rocketry and/or nukes consider the general population freakishly paranoid, knee-jerk, and ignorant about the dangers of both.