It's absolutely authoritarian, it's setting conditions ok your life outside of the boundaries that have any relevance to your contract.

Authoritarian is typically applied to the authority of the state, but regardless the argument would be that they dont want to be seen as doing business with people they believe violate certain moral standards. That doesnt excuse the accusation you actually made, regardless.

And they did apply it to the state (federal government) because they're using it as an example in defense of the actions of the federal government.

The law routinely distinguishes between when the state acts as a general employer vs when it acts as the state. A police force can fire an officer for statements they deem inappropriate even when they would otherwise be protected speech, as an example, because in that situation they are acting as an employer, not as the state. You wouldnt argue that you cant fire a police officer for supporting nazi beliefs in their off hours, right? Do you believe endorsing firing that officer makes you a statist or authoritarian?