Clubs can set any rules they like. If you don't like them, then don't join.
Aero bars are for TTs where you don't ride in groups. Being on the bars with people around you and on less then ideal roads can cause you to have control issues and take someone down with you.
It's totally different when you're on the road by yourself and have a clear view of the conditions and surface.
BTW... I assume a Cervelo S5 and not a Trek Emonda S5.