Respect and reputation are extremely important in the polite Victorian society of An Ideal Husband. The respect of your peers gets you an invitation to dinner and a potential opening for what it is you really want: a promotion, a husband, more invitations to dinner, etc. Decorum is so ingrained in these characters that they can't talk to their friends in front of the butler, and can't order the butler in front of their friends. Characters who flout social norms are punished or woefully misunderstood.
Lord Caversham's verbal abuse of his son reflects Victorian England's worship of surfaces.
Mrs. Cheveley's bad-girl status helps her gain access to what she wants.