Anyway, republicans appeal is mostly towards security and group cohesion. It's both positive and negative, although recently the negative aspects have gained dominance, since religion and war is a useful way of creating locked in voters (I'm talking 25+years, not just the last decade).
So, in response to the OP - people vote republican because they like the message. And yes, that's the same as the other side. The "why republican" is just a reaction to the opposing message, and it's reinforced by the... less ideal... republican party that has been recently in power.