A thumbs-up/thumbs-down approach, even if anonymous, seems like it would cause more divisiveness, so I don't want to try that experiment. Besides, I'm not sure a convenient plug-in solution for that exists.
However, it is apparent that the Thank You feature was more controversial than I expected. It seems to work well on some other boards where I participate, but perhaps this forum is different.
Maybe I'm reacting to a vocal minority, but I'm disabling the feature for now.