I can't recall off-hand anyone here or elsewhere objecting to using nuclear bombs to deflect asteroids. Even the most rabid environmentalist can do a risk analysis on that one.

Still, as others have pointed out, there may be more effective ways of accompishing the same goals. More AI-intensive solutions have included gently parking a mining machine on the surface and firing chunks off it using a bucket accelerator. A nuclear rocket using melted ice as reaction mass might be another solution.

If you catch the asteroid soon enough, even the smallest push might be enough to nudge it into a safe course. Solar sails and ion engines start to come into feasibility.

I'd like to see a large nuclear space probe built with ion engines and a mighty shitload of propellant which has the sole job of visiting as many suspect asteroids as possible and tagging them with tracking beacons. Given that we can figure the exact trajectory and speed of the Pioneer probes by analyzing their zillionth-watt-at-Earth signals, this would not take a very powerful transmitter.

It goes without saying that the same probe could do a lot of science along the way.