"My mother was a muggleborn--born into a nonmagical family. Family members get to find out about the Wizarding World if they have a loved one that's born a witch or wizard, so my aunt found out about magic when my mother got accepted into school." 
 
Harry, by no means, thought all muggles were the same or thought they'd all be intolerant, nor did he feel that they were inferior, but he did think there was great potential for conflict, and that was on top of conflict that was already happening.
 
"As for a common enemy, think about how even contacting muggles to fight Voldemort would've gone over. 'Hullo there, muggles, this one evil wizard and his pureblood supremacists want to kill and subjugate you all--mind helping us out with fighting our war against them? By the way, we're a society living in secret underneath your own, and we've all got potential for incredible power like they do.' That's not even getting into the fact that with a war going on, our government was taken over by people that believed in hunting muggles for sport. Neither side was ready for the other, I don't think."

He finally moved his queen, taking one of Howard's knights.