It's not clear to me what the modern concern would be with nuclear powered military rockets. ICBMs don't have particularly high performance demands by modern rocket standards, and modern ICBMs are built with solid fuel boosters because they're simpler to deal with in every way. A nuclear powered ICBM doesn't make much sense; I don't think they'd make those and if they did, I don't think they'd be more alarming than the ICBMs which already exist.

So what would the military even use such engines for? Maybe an X-37 successor, but why would that be particularly alarming?