This came up on the Turks & Caicos Aggressor II back in April 2018. Another diver and his wife were onboard, and he (I think they, but at least he) had a side mount rig and wanted to dive side mount. Captain was under the impression Aggressor Fleet didn't allow it, so he ended up using a rental from them. At the end of the trip back in port, it turned out Aggressor Fleet didn't mind him using a side-mount BCD, but he could only use one tank. So they didn't charge him for nitrox and the Captain was apologetic about the misunderstanding.
I just checked the 'Know Before You Go' sheet for that particular boat; it says all dives should be planned as no decompression diving.
Since a side-mount rig with 2 tanks is, in effect, 'doubles' diving, I wonder if that's a concern? Or space a 2-tank rig would take up on a boat not set up for it? I wish Aggressor Fleet had a rep. post on the forum; it'd be interesting to hear their reasoning.
Richard.