blah, blah, more of this make it like the comics nonsense, you really can't stop playing that record, can you?
We didn't know the exact extent of the Hellfire Club, just that it had one public face as a casino/club in that scene...
It matches the description from the Marvel wiki:
Today, the Hellfire Club is an overt, worldwide organization. Famous for its lavish annual gala, it is open to the wealthiest and most influential entrepreneurs, politicians and socialites, whose membership is traditionally passed on to the heirs of their estates. Within the Club at large is a secret cabal, known only to a select few. These Inner Circles, of which there are typically one or two at a time, desire to achieve world domination through political and economic influence, subversive activities and the recruitment of mercenary forces and powerful superhumans.
Now quite clearly, powerful people like the Colonel went there and we saw the Inner Circle of Shaw, Frost, Azazel, Riptide. We couldn't get the entire history of it in one film; it's taken the comics decades to establish its full backstory. To expect much more in this film is being a bit picky. You can't fit EVERY detail about EVERY character and scenario in every film. This is a typical complaint from diehard comic book fanatics who can't accept economical storytelling and want a 20-hour movie.
So it would've been silly and taken to long to establish a bit of background to the club and have Shaw with political influence because of his wealth and Corporate dealings?? If you say so.