The last space race ended almost causing a nuclear war between Russian and USA. It was so close that it was prevented from the disobedience of one guy to push THE button.

That was the nuclear arms race. They may have been intertwined to some extent, but they are still two distinct endeavors.

Sure, asteroids are dangerous but there are far greater dangers here on earth.

Sure. But you wouldnt want technology to get rid of those.

They would eventually come to existence whether they were sponsored from the military or not. I made this argument in an earlier post. Science progresses in small steps. If it wasn't for Einstein then another guy would fill in. If it wasn't for the military the funds that push the research would generate similar outcomes.

Of course. But how much longer would it have taken? 100 days? 100 years?
How much spacerelated funding is there if you take away military or military-related funding? (That includes NASA, ESA and every other space agency even if they don't count into the defense budgets)
How much research money flows into prosthetics if you takeaway military research budgets in that field?
Point being: any technological research funding is beneficial. It's not a very efficient route but the world is full of stupid so it is what it is.