While it may be technically correct in the context of US Constitutional law, people that make this claim expose their opposition to the wider concept of free expression and likely would be the first ones to support an amendment to weaken the 1st amendment
I'm not going to engage further with someone who acts like that.
it is rejection of the idea of Natural Rights for which the US was founded on, this rejection of natural rights is growing in the population is is very dangerous to those very rights
Believing that only governments can censor is a rejection of the principle of free expression which is "I may disagree with you but I support your right to say it"
Society should not embrace the idea that businesses, employers, etc should choose who they transact with based on peoples opinions and views. Society that embraces these kinds of virtue tests have no liberty, and have no free expression