Well, I've been writing computer programs since 1979, and I'm neither a cryptologist nor a mathematician.
There are certain types of programs (graphics for example) that require a high level of math, but in the main, programming requires a good grasp of logic and language (IMHO).
Since cryptology is the science of secret codes and cyphers - then no, you don't have to be a cryptologist to be a computer programmer. But yes, cryptology will in itself often involve the use of quite involved mathematics.
However, If you want to write any computer program that uses maths, then you have to know how to do the maths on paper before you can write the operation as a program. Obviously you have to understand fully what it is you're trying to do.