Most cases regarding the First Amendment usually deal with claims about the government infringing upon free speech rights or the establishment clause. A lesser known issue with the First Amendment is whether the government can compel individuals to certain kinds of speech.
During World War II, many states passed laws forcing public school students to salute the flag as a way to pledge allegiance to the United States and its war effort. The Supreme Court in Minersville School District v. Gobitis upheld the flag salute laws against a challenge from Jehovah Witness members who refused to salute because it infringed their right to exercise religious freedom. The law in question was upheld because the flag salute applied to every student regardless of religion, and at the time, there was a valid governmental interest in fostering patriotism during the war effort. As a result of Minersville, many Jehovah Witness members continued to refrain from saluting the flag which led to various acts of violence. The court hadn't anticipated the immense backlash against the religious group for not saluting the flag.
A new case arose under West Virginia State Board of Education v. Barnette where a member of the Jehovah's Witness again refused to salute the flag, but instead of claiming religious exercise, he claimed constitutional protection against the flag salute law through the First Amendment's free speech clause. The Supreme Court realized its mistake from three years earlier and overturned the Minersville decision. This decision invalidated laws across the country that required public school attendees to salute the flag. The court recognized that individuals could not be compelled to have a certain viewpoint by the government as it would infringe upon one's speech rights.
In 1977, the Supreme Court dealt with a compelled speech case regarding license plates in Wooley v. Maynard. The Maynards, who were Jehovah's Witnesses, objected to New Hampshire's motto, "Live Free Or Die" which was displayed on the plates. In objection, the Maynards cut out the phrase from their license plates. The numbers and characters on the plates were still clearly visible. However, New Hampshire had a law which forbid the obscuring of the state motto on its license plates. The court ruled in favor of the Maynards as the state's interest was not compelling enough to infringe upon the deep and sincere beliefs of the Maynards. Therefore, the state could not coerce the Maynards to put the license plate on the car with the state motto.