How important is the reputation of one's undergraduate institution? I attend a state school, specifically a California State University (CSU) for those of you who are familiar with the California public school system. I am hoping to offset this with a strong GPA, letters of recommendation, and GRE scores. I have also worked two professors as a research assistants and have completed a research internship with the McNair scholars program. Would this overcome the reputation of my undergrad institution?
Yes, it can. You have all the hallmarks of a good grad-student-to-be.
It's all a giant crap shoot at some level. There are people making these decisions. They are just as weird as your extended family. People are strange fickle creatures.
The admissions committee chair might have dated a vengeful bunny-boiler from your undergrad, and if so, there's not a damn thing you can do to make them admit you because they have a visceral reaction to the name. You can't control that.