Certainly. Of course.
Long planned to take Millennium repo cruise to Barcelona in late April/May and have no intention of cancelling. From Barcelona we'll go to Madrid and London before returning home.
It is trite to say that if we cancel they've won, but it has an element of truth to it.
As for how we are treated, I've long been of the opinion that generally we get what we expect when we travel. I have a number of friends who were abroad on 9/11. The one who was in Nice reports that her hotel set up a special section of the bar with a TV set tuned to CNN and more or less reserved for Yanks. The management were very solicitous, friendly and compassionate, and most drinks at that bar were never billed. Plus they were given a heavily discounted room rate until Air France could get flying again.
If many people in other lands don't care much for us it's generally because so many of us have worked so hard to deserve their ire. You can only live on the "we saved your butts in WWII" thing for so long.