That's not a point in favor of why they coexist. The military is going to fund uranium mining one way or the other, given the potency of nuclear weapons as a deterrence, as well as their own militarized applications of nuclear reactors powering aircraft carriers.

The only valid argument for why military planning influenced civilian nuclear power because the military also tested and decided on nuclear power for various applications because it was efficient, reliable and had long term viability with minimal space investment. But even the military came to the conclusion it wanted nuclear power where it could get independent of wanting nuclear weapons.

Edit: And as a bonus, just because this myth is so dumb, Chicago-1 predated the Manhattan project and is directly cited as being an inspiration for the Manhattan project, not the other way around as people keep trying to claim. Even without nuclear weapons we would still have uranium powered nuclear reactors, and they'd probably be more prevalent without all the fearmongers hopping on the big oil bandwagon and spewing propaganda that couldn't be further from the truth.