While that issue hasn't been specifically tested in court yet, the current interpretation of the First Amendment probably wouldn't allow the US government to dictate the types of speech you're allowed to put in your LLM. But federal government purchasing decisions aren't generally bound by the First Amendment. In other words, government officials can generally refuse to purchase your LLM services if they don't like the speech it outputs. So there's no real constitutional concern with this EO.

I'm not claiming that this EO is sensible or enforceable, just that it's not prima facie unconstitutional.