Is there a quick and easy way to modulo-2 add two binary files together to get a third file?

How do you mean exactly? As in treat two identically sized files of size N bytes as two 8N-bit numbers, which added together give an (8N+1)-bit result? or treat them as an array of 8-bit (or 32-bit) numbers, and add each byte or word separately, modulo 2^8 (or 2^32)?

And what to you want it to do when the files are different sizes? And how do you want to handle endian issues?