Comparing Sophia's and Felicia's situation doesn't make sense. Sophia isn't a Carnation; she is Abel's protege, because she has exceptional talents and skills (and inventions) that are useful to him. As long as she and Abel are in cahoots, she doesn't need the other patrons to like or trust her, and indeed I suspect that they don't.
Felicia doesn't bring any of those things to the table. She's just gambling on the notion that once she has a membership card, she'll be able to schmooze her way to the top. And the other patrons have little reason to regard her as just another Carnation, simply because she wins the contest (assuming she does) and gets a card.
The situation is quite different. Sophia is Abel´s chosen heir for a bundle of reasons. If she desires to, she can bring a lot of stuff to bear, for the vast majority of members Sophia is too big a fish. Even Chuck, who is sad that he cannot do anything permanent to her, should he ever win (doubtful that this happens before the hostile takeover takes place), since Sophia is too valuable.
For the gangbang we should remember that Sophia was convincingly costumed as a house girl, very few members will make a connection at all. Hell, most players did not know until TD confirmed the speculations. But beside the powerful backing Sophia has there is another point to make. Unlike Felicia, who is charming and can win sympathy rather easily, Sophia is an eccentric who cares not much about how she comes across to others. it is one reason I do not believe Sophia was chosen by Abel to honeytrap Edwin. Sophia is honeytrap material only for a small minority of guys. That Edwin and Sophia can click together is simple chance at work.
Even our resident full sadist Kathleen is unnerved by Sophia´s manner. Like she said "Besides, two is better than being alone in that woman´s company". I doubt many club members like Sophia, but it is not important to her anyway.
Felicia on the other hand is, as said, charming and has some useful knowledge.If she becomes a club memeber she certainly will have chances to get what she wants. Too many of those members will want to get an advantage for their own career/business. If Felicia can deliver such an advantage from her knowledge 9 out of 10 members will bite. She does not need to win a sympathy contest, if she has useful knowledge, the connections she makes in the club will help her gain what she wants.