How to refer to a person who is not from science background?

You are of course considerate not to want to offend your conversation partner. But whatever word you use to replace "non-science guy", you'll be taking the curious approach of informing someone that you're going to say something that he won't understand. However you say it, this kind of suggestion implies that the listener is deficient in some respect.

Instead, you might try something like this, "This may all be a little arcane, so please stop me if you'd like for me to explain something I've said." In other words, you could call the subject you're discussing obscure, rather than calling the listener uninformed.

You can refer to someone as "An MA" just like I could be called "An MPA" for my terminal degree. Since SE likes sources, the OED has this sense as definition #15 for "Master."

I suggest being more specific. If you don't want to be offensive, instead of saying what he/she isn't (a "science guy") emphasize what he/she is. For example, if this person has an MA in English literature, you could say "You're a Master of English Lit" or "You have a Masters in English Lit." If your point is to say that the person isn't an expert in a given field, you can say "You have a Masters in English Lit but this topic requires more experience with computational astrophysics."

I believe 'humanities' is your best bet. It is a general term for rigorous inquiry and academic pursuit that is not grounded in the natural sciences. Religion, philosophy, language, arts, music- I would throw in economics and political science, because these disciplines rest on human behavior, are driven by psychology and cultural norms. (The actual practice of hard sciences is too, but that's another matter). So the counterpoint to "science guy" might be one "from the humanities school" or "steeped in the humanities."