During Liturgical Celebrations, Bishops (even Obas) are seen with cap/hat on their heads when the scripture says, “Every man who prays or prophesies with his head covered dishonours his head (Christ) 1 Cor 11:4-5.
Why should these people be exempted from this?

It all started after the Council of Nicaean by Constantine.

Let me share here what Joyzy Pius Egunjobi wrote about this issue:

Crown and Turban are mentioned in Exodus 39:27-31 and Leviticus :7-9 as part of the vestment of Aaron (the High Priest). The Lord also told Aaron and his sons Eleazar and Ithamar, "Do not UNCOVER your heads nor tear your clothes, so that you will not die and that He will not become wrathful against all the congregation… for the LORD'S anointing oil is upon you." (Lev 10:6-7). Though there are no Biblical records, artists often depict the Apostles and the earliest saints who were bishops wearing “zucchetto” (skullcap worn by bishops) or the Miter (The headdress/headband worn by bishops). The Miter is a sign that the Bishop is the head of a particular Diocese though the Bishop himself is in subjection to the Headship of Christ (Col 1:18; 1Cor 11: 3) - the very reason he (the Bishop) removes both the skullcap and the Miter during Consecration. Symbolically, Miter stands for the Crown St Paul talks about in 2 Timothy 4:7-8 worn by the Bishop who leads his flock in the race to salvation. “For no man takes this honor to himself, but he who is called by God, just as Aaron was (Heb 5:4). When you look at the Bishop presiding over the Mass therefore, see in Him the Supreme Head and High Priest, Jesus Christ, listen to his teachings, observe them and do them (Acts 2:42; Matt 23:3).