Final answer:
Wearing a political button to work at a private firm is most likely considered protected speech, as the First Amendment provides strong protection for political expression, though there may be limitations within the private sector.
Step-by-step explanation:
Among the options provided, wearing a political button to work at a private firm is most likely to qualify as protected speech. The First Amendment to the U.S. Constitution provides robust protection to political speech, which includes symbolic forms of expression such as wearing political buttons or armbands. However, this protection can be subject to certain limitations within a private workplace if the employer sets specific dress codes or policies.
Shouting "FIRE!" in a burning building is not protected speech as it doesn't contribute to any form of discourse and may not cause panic since the situation is already clear. Publishing an article specifying future terrorist attacks may be regarded as incitement to lawless action and therefore not protected. Hanging a sign promoting criminal behavior on a locker at school is likely to be considered incitement or promotion of illegal acts, thus also falling outside the protections of the First Amendment.