Germany had women's suffrage in 1919 and proceeded to go to war against almost everyone. Poland, Norway, Russia, UK, USA, Netherlands, Sweden, and other allies all had women's suffrage by WWII.

Wikipedia: women could vote in the USA since 1920, and in the USSR since 1917. Though the Cold War was more of a series of proxy wars and an arms race.

But the argument in the grandparent post is not supported by history either. The military monk orders of the Crusades are just one example.