Sorry, Just saw this message.

Yes, "that" is optional when it is used this way.

But it is not optional when you say: I am one of the students that really like Prof. WQ.

Hope this answer your question as well as your guess about "帶藍色小禮帽的某教授" (do you mean WQ?).

Also, Prof. WQ sent me a QQH yesterday asking me to stay with the translation class, at least before she comes back. I can try, but I wish I had as much time and energy as Prof. WQ.