A debate about campus speech codes

I have completed my debate with Greg Lukianoff and others. I ended up being perplexed about what Lukianoff believes and what his organization, FIRE, stands for. He says the “First Amendment” but the First Amendment protects speech codes in private universities; it doesn’t block them. So he says “in the case of private colleges, First Amendment values.” But he never addresses this conundrum: why would the First Amendment protect speech codes if speech codes undermine First Amendment values? Imagine that a Republican congress, under the leadership of a President Trump, passed a law compelling private universities to abolish their speech codes. Would FIRE defend the private universities against this form of government censorship or congratulate the government for advancing first amendment values on college campuses?