Are teachers allowed to say shut up to students?

Absolutely! If a student is making a noise while the teacher is trying to educate the class, the teacher has a right to demand a student be quiet!

Teachers are human like everyone else. When pushed by disrespectful students, it is expected that they will demand compliance, and shouting "Shut Up!" is sometimes just enough to get the attention of those misbehaving. The wise teacher, however, will use it sparingly.