It's important to remember that the Constitution is, in effect, more than just the text as you read it. All parts of the law, but particularly the Constitution, are "interpreted" by the judiciary, and these interpretations have the force of law. In particular, the First Amendment as interpreted by the courts is a lot more complicated than just what it says.

For example, your strict reading would suggest that the states could make a law restricting freedom of speech (&c). But the Supreme Court ruled in 1925 that the First Amendment precludes such actions by the states:

https://en.wikipedia.org/wiki/Gitlow_v._New_York

Just like a private company can have speech codes without running afoul of the first amendment, so can the US Government for its employees. That's all it is - not some law, but an employer mandate.

The first amendment applies to law governing speech.

TFA even points out that the tweeting is only verboten if associated with the gov dept.

Weird that it's EPA-only, though.

I'd say it's more analogous to a boss telling you not to post with the company account.

Twitter accounts belonging to government agencies represent the government, not individuals. Individuals and the press are the ones whose free speech is protected.

The president can't issue unconstitutional executive orders but has great powers over the executive branch which this falls under.

Right. He can't stop you from saying what you want to say. He can stop you from saying what you want to say on an official Federal government platform.

For that matter, many employers can do that. I can say whatever I please, but not with my company name on it.

Exactly, can't believe so many people here lacking basic understanding of professionalism. You can't use office account to deliver your personal message.

We'd need a specific example to determine if the communications were a personal message, raw data supporting climate change or (unlikely) 5 sigma confidence level results in say a temperature trend.

Personally, I struggle with the idea that scientists working for the federal government have to report to or be muzzled by the current administration. I see these people as working for the country not for the administration but I'm naive and optimistic in general so I'm sure many people will point out that it would be a crazy way to run a country.

In the Canadian case, scientist needed to request permission to attend conferences months in advance and, from what I understand, if there was the least chance of bad press coverage from the scientific results being presented, then the person was not allowed to attend. I believe there was a similar muzzling of attempts to publish in peer-reviewed papers. That sort of thing is clearly not acceptable behaviour for a government administration. Government organizations like the EPA are not companies trying to maximize profit by selling a widget, they are researchers and regulators trying to determine the best path for everyone in the country with respect to economics, health, and environment.

He absolutely can, they just might not hold up three years later when it finally makes it to the supreme court (or they might depends on who's there)

Depending on the jurisdiction of the lawsuit, the judge (or panel of judges) will probably have the right to file an injunction which can prevent even the president from doing something. The Republican party got into the habit of using state Attorney Generals to sue the Obama administration and the resulting injunctions drastically slowed or killed some aspects of his policies. You can bet many of the Democratic party AGs are just itching to do the same thing, especially those with political ambition in heavily blue states. I don't know if the President has ever been held in contempt but it's a reliable process for preventing policy implementations.

I think this order's authority probably comes from the fact that Trump is the head of the Executive branch, not from any legislative power. That is, they're in a boss/employee type relationship.

Presedential power has grown a LOT in the past 50 years. I still think we have a strong enough constitution to prevent a Hitler, but not as sure as I would have been in the previous generation.

It almost entirely depends on the willingness of Congress to enforce the rules, and more importantly the spirit of the rules.

I say "amost" because the Supreme Court has a part to play, but it's in a bad shape right now (highly polarized, split 50-50, with an opening for just about any old stooge to be helicoptered in).