We see article after article in the US with wringing hands over how Europe thinks about us. As you pointed out Europeans in general have a negative attitude about Americans and think we are all ignorant and insulting even though all most of really know is what they see TV and what they saw during their week in Orlando. So I am saying America needs to ignore the idiots who do the hand wringing and tell Europe to go collectively fuck it self because we should value their opinion at the exact same level they value ours. One of the advantages of being a super power is the other guy needs you more than you need him.
The problem is Europe has been living under our protective presence for so long they think they not have right to it but the right have opinions about how we run our country. How many Europeans would welcome the US taking a keen interest in the internal affairs and not only expressing those opinions but believing they should be given weight?
You right that Europe's reaction is to be expected but so is a backlash to that opinion.