Which activity is protected under the First Amendment?

Filming police from a distance and in a non-interfering manner is protected under the First Amendment because it falls under the category of freedom of speech and the right to gather information about public officials performing their duties in public spaces. This activity is considered an exercise of the public's right to document governmental actions, which is a crucial element of transparency and accountability in a democratic society.

The First Amendment protects various forms of expression, and recording public officials, such as police officers, is viewed as a form of speech. As long as the filming does not obstruct the officers' duties or invade privacy where there is an expectation of privacy, the act is generally permissible.

The other activities mentioned, such as protesting on private property, threatening law enforcement officials, and posting defamatory statements online, may not be protected by the First Amendment due to limitations placed on speech that may infringe on property rights, involve threats, or constitute defamation, which is not afforded protection under the auspices of free speech.