Ok I am idolized by the White Glove society, and I have done Beyond the Beef, yet I have no option to be inducted to join the White Gloves society and gain access to the members section, is this a bug or am I missing something here?

im pretty sure u hafta join them while doing beyond the beef, if u complete it by some other means, u may not be able to join after its complete. also u need to be recognized by the strip, so if ur fame with the strip faction isnt high enough it may not let u join.

I am also idolized by the strip.