The problem here is that there's tons of different "flavors" of Christianity/Islam/whatever. In fact, the term "Christian" is just silly to begin with how we use it. Penn Jillette talks about it a bit in a bigthink video, it's pretty interesting and I highly recommend watching it (4:50 in for relevant information). Thing is, sure MLK was a Christian. But there's even Christians out there today (extreme right wing ones, but still) who suggest that King was not a Christian. Just Google "Martin Luther King Virgin Birth". It's been brought up before (I believe by Hitchens, just for example) that King didn't believe in the bodily resurrection of Christ OR the virgin birth. These are considered central tenets of Christianity to most Christians.

Then you have the split of Sunni/Shia Muslims. Then you have Muslims who think that certain things in the Hadith/Quran are just sort of recommended, not necessarily "dogma". Terms like "Christian" and "Muslim" are not very helpful, as their definitions are becoming more and more nebulous. King was a great Christian to many, yet he believed things that, to many, are completely heretical and blasphemous. Comparing Martin Luther King, Jr. to say, Pat Robertson and saying "see! there's good ones and bad ones!" is just silly. It's apples and oranges.