Then I guess it means I wouldn't have used the term personal beliefs here because the quote uses the word religion and there is no context to tell us that what he meant was something other than the usual definition of religion. Either the quote does not accurately represent Luther king's belief and needs clarification, or Luther king's belief that religion and science cannot be rivals is wrong. In any case, I would think that quotes are supposed to be self explanatory and on its own, this one sounds wrong.
Indeed, the fact that personal beliefs can always possibly conflict with science is not particular to religion, which is one of the reasons why I think we can take this quote at face value. Another word could have been used instead of religion if the intent was the same as yours but Luther king's chose the general concept of religion. Doesn't it suggest the intent of not talking about all personal beliefs but rather to focus on a more specific instance ?
I would also add that if the purpose was to talk about all personal beliefs, he wouldn't have said that, because it's obvious to anyone, and nobody would quote him for that reason (At least, it would be very unlikely).
To me the quote is all wrong. If Luther King's intention was to suggest what you are suggesting, I am then on board with you too, obviously. But nothing really shows that in the choices he made when formulating the idea