So today at school (I go to a public high school in Texas) a substitute teacher told a kid to stop saying Jesus Christ. I was wondering if the teacher has the authority to do this? It was clearly for religious motives as the kid wasn't being a distraction or breaking any rules.
This is a pretty good guide to the student's right to express their views on religion (for or against). For example you may pray in school, but you cannot compel others to listen to your prayers. You may discuss Jesus Christ and you may advocate a religious perspective, if it is on topic (e.g. in a class discussion abortion, but not in an algebra class).
There are familiar ways of saying "Jesus Christ" which would be disruptive, but a general prohibition against uttering a name (on the grounds that the name is of a religious figure) is not a proper application of the separation of church and state -- as the ACLU statement says, SCOTUS did not make public schools religion-free zones. Whether or not the teacher was given the authority to forbid mentioning religious figures by some supervisor, that would not have been proper authorization. Official advocacy of religion in general, or a particular religion, is contrary to the First Amendment, as is official prohibition of religion in general, or a particular religion.