On the far left, there is often grumbling that we don't celebrate Martin Luther King, Jr.'s legacy in toto. King was a socialist, and stridently antiwar. This tends to get swept under the rug; if it didn't, it would be hard to countenance a national holiday. That part of King's legacy belongs only to the left.
What we celebrate is not what is divisive but what is unifying about King's legacy: his fight for equality against racism, his dream of a colorblind society -- what can be plausibly described as "King's Conservative Legacy," but which of course is bigger than that.