I haven't seen very many people on a charter boat with doubles unless there is a planned tech dive, however there have been a few occasions, and usually the biggest issue is the tank holders, and how to stow the tanks. If they are using the "cup" style holders, it can be an issue, but you simply work around these things. Im interested in what charter operators have to say about this. I doubt too many charters are going to flat out turn you away because of your doubles. In my limited experience with this they will ask you to limit your dive time if they see you with lots of gas, and/or ask you not to go into DECO, and that is all reasonable and understandable. It would be nice for some actual charter operators to chime in on this.
When I lived and worked in Key Largo in 90's, our shop had a good relationship with Paul at Quiescence before he died. At the time, some of the staff members were doing technical diving including the use of doubles, triples, and rebreathers. Several years ago, a friend and I drove to Key Largo from cave country to do some ocean diving. Some blonde woman running the show for Quiescence wouldn't let us on the boat with our UWATEC digital gauges and made us rent dive computers. As we unloaded doubles from the SUV she flat out refused to let us dive. I haven't been back. Maybe the shop has a new policy, but they lost my business. I only dive with Chris Brown at Silent World when in Key Largo knowing that Horizon Divers can accommodate me if Chris can't.
My advice is to check ahead anymore if you are unsure of an operator's policies. You'd think this would be less of an issue as technical diving grows in popularity, but many operators have polarized themselves as "recreational" as defined by the typical single tank + poodle jacket. But, in my experience Quiescence was the only dive center to just say no to doubles.
I worked for 3 charter services and only when I was living on Cayman Brac did I never see doubles on a boat.