Which laws in the USA don't allow freedom of speech?

Legally, there are limitations to US citizens' right to freedom of speech in the workplace, as members of the armed forces, or as elementary or secondary school students.
In almost all states, an employer can fire an employee without showing or naming cause. Employees are protected from being fired based on race, gender, and so on but not based on their opinions, whether on politics, company practices, or even sports.
People are also frequently fired for trying to join or form unions. In theory, that's supposed to be protected by the Wagner Act. In practice, that law was gutted by the later Taft Hartley Act, which made it legal to not recognize unions with "radical" members, like socialists. Most agencies dealing with labor disputes are staffed by pro-business members, if they are staffed at all.
Those in the military have their speech severely limited. It's common to be punished for what's viewed as insubordination, in the name of military order. Members also are limited in how they can participate in the political process while in uniform, backed up by court martial. There is also a strong custom, backed up by law, that active duty military officers stay out of politics. The alternative would be a place like Latin America, where the military often takes over to decide the nation's fate, often by force in dozens of coups.
The courts have also ruled that students' speech can be limited by administrators in the name of order. This includes hair and dress codes. The main remedy is in appealing to parents through school boards.