Dear Mr Dawkins.
Thank you very much for what you are doing in promoting reason over, well, other things.
May I suggest you a line of argument in the following situation. You seem to often hear questions like “How could Christianity (Islam…) be wrong if such great things came out of it”. It seems to me (although I may be of course wrong) that your usually rock-solid arguments at this point become less solid, and an experienced and clever opponent might (and probably do) take advantage of it.
However, as you obviously know, from the point of view of logic false assumptions MAY actually lead to true statements, as well as to false ones. It is only TRUE assumptions that can logically only lead to true statements. So, Martin Luther King being good does not mean that religion, on which he presumably based his views, is true.
This idea may not be easy to formulate so that the broad audience would find it convincing. I certainly failed to do so: I console myself with the fact that English is not my native tongue. There is also still a lot to be considered (e.g. how do we know what statements are “true”, and how their “truthfulness” is related to them being “nice” or “agreeable”) before one can use this idea in the argument. But you may find the mathematical fact that false assumptions may equally easily lead to both “true” and “false” statements be worth considering for use in your future battles.