These are professionals, so they absolutely should...
must teacher's also wear school uniform
No, I do think there should be a dress code. No mistake. But a uniform would mean all the male teachers dressed the same, and vice versa for the female teachers. These are professionals, so they absolutely should maintain an air of professionalism, but uniforms wouldn't be in any way helpful. As far as for students, if a teacher is judging them on their fashion choices, that is a whole separate issue. But some sort of dress code should apply. Like, no ripped clothes, no underwear showing, etc.