I am sorry to inform you, but Martin Luther King was not a conservative.* I know you would like to believe that he was, in order to justify your current movement as a "continuation" of Dr. King's work. But let me stop you right there.
Please do not complain that the civil rights movement has today become "liberal." It was, I assure you, liberal from the beginning. Even radical. You can say, "Well, I chose to get out of the movement *here*." But don't say that it gotten all scary liberal. No, it always was. Conservatives always fought against it. What's changed is that you've joined them.
And that's fine, just be honest about it.
*yes, he was more conservative than other members and leaders of the civil rights movement, but he himself could certainly not have been considered a conservative.