I have a BS in CS, Math and Stat, and a MS in CS. I've been a developer for a long time and worked with a lot of other developers. The biggest determinant IMHO to becoming a good, competent developer is the desire to become an even better developer from reading, experimentation on your own time, and an open mind.
If you have that kind of passion for software development, you'll do fine, regardless of your original degree (or lack thereof). Having said that, I'm skeptical of the value of a MS in CS without a BS in CS. In my MS program, the assumption was that you had the basics - algorithms, data structures, language theory, basic hardware design & logic, compiler design. You can certainly gain that knowledge with enough reading on your own, or taking some courses at a local community college to get the basics.
This is what I did. I have a BS in Politics and a MS in CS. Before taking the MS degree, I read a lot of the books one would read for a BS in CS and did a lot of programming. This prepared me well. I met others in the program who didn't and it showed. Taking Masters level courses without background will get you lost really fast.
If you have that kind of passion for software development, you'll do fine, regardless of your original degree (or lack thereof). Having said that, I'm skeptical of the value of a MS in CS without a BS in CS. In my MS program, the assumption was that you had the basics - algorithms, data structures, language theory, basic hardware design & logic, compiler design. You can certainly gain that knowledge with enough reading on your own, or taking some courses at a local community college to get the basics.