The addition of that phrase, "Under God," was done under the Eisenhower administration, and was widely regarded by many as being a political ploy. Lots of people objected to the insertion of religion into the Pledge, and still do. Some of them refuse to recite the Pledge at all for that reason; others go silent when those two words are spoken. You can actually hear the voices drop in volume.
Probably the worst thing about sticking those words in was the crass politicization of profound religious feelings. What is the harm? Well, if you believe that reciting such a pledge is a sincere statement of loyalty and belief, it is forcing people to swear allegiance to a religion that may not be theirs. If this seems trivial, try substituting the name of any other deity and think about the "cultural values" of being forced to swear allegiance to him/her/it.
At the time, it didn't seem that awful, but now in retrospect, it does. I'm glad we've evolved away from it.