I think the fundamental difference between a nuclear sub or other ship and a nuclear rocket would be where things can go wrong. If a nuclear boat has a reactor problem, that reactor problem stays on or under the water, pretty much localized.

With a nuclear rocket engine, it's likely to fail inside the atmosphere and in a way where it fails catastropically that doesn't even necessarily involve the engine itself being the cause. One faulty heat shielding tile? Congrats, your rocket disintegrated on re-entry and spread fissile material in the upper atmosphere for hundreds or thousands of miles.

That's why I think nuclear engines specifically for space travel are a bad idea. The only way to make them not a problem is if you assemble them in space and the ships with them are never leaving space, while getting the fissile material from, like, the moon. Which is something we are decades away from even entertaining as a species.