Would UC's take you out of running if they see a C and B I received during freshman year?

You submit all grades from all a-g courses taken 9-11th grades. The grades from 9th for the a-g courses are checked to make sure you passed and they fulfill the a-g requirements. They calculate GPA based on 10-11th grades and weight the UC approved Honors/AP/IB or DE courses taken 10-11th grade. They do not weight your Freshman courses even if you have taken UC approved weighted courses.

A C and a B Freshman year for an a-g course is passing so no it will not take you out of the running.