Conditions for admissibility are one thing, and you can be denied entry for any thought crime that the government wants to impose.

Once you are in, you have the same rights to free speech as any citizen, and the same rights to due process as well. In fact, the only thing they can do to curb your free speech is prove in court that you lied on your application. Which is likely how this case will play out after judges rule on how illegal their attempted action is, but as of yet the government has not provided any evidence of him lying on his application.