You lost me here.

How can the government have a monopoly on speech if we're talking about the government being prevented from saying things by a judge?

The Supreme court has never said anything like what you just typed in 200+ years of american history. Do you type this every day, constantly knashing you teeth at the existence of trade secret laws, copyright laws, libel laws, and the like, or does the rheteric come out in service of special goals?

If I profess those same beliefs while acting in a public capacity I am infringing on the rights of others by favoring or creating the impression of favoring a particular religion.

You individually have freedom of association. If you don't like gay people, or Vietnamese people, or MAGA republicans - ultimately nobody can make you be friends with them in your private life. However, acting in an official capacity you're absolutely obliged to be neutral.

The government very rightly has restrictions on how partial it can be as it is the arbiter of our society.

We’re talking about the government coercively censoring speech of citizens in/on the media, not under emergency orders or commandeering, but as a matter of routine. Yes they’ve always done this even with the major news networks thirty or forty years ago (pre-Internet). It was wrong then just like it’s wrong now. It’s more visible and obvious now to more people, the evidence is right in front of us through leaks and email disclosures from efforts like the Twitter files.

But their right to free speech ends when they start to hurt citizens' rights to express themselves.

Is free speech important solely because it protects you against a malicious government and therefore there's no issue at all with non-government entities censoring others' speech and no reason for the government itself to have it? Or is it important because the marketplace of ideas confers some societal benefit and it would be better if agents of the government were equal participants in that market?