LADY BRITOMART [squaring herself at him rather aggressively]: Stephen: may I ask how soon you intend to realize that you are a grown-up man, and that I am only a woman? STEPHEN [amazed]: Only a— LADY BRITOMART: Don't repeat my words, please; it is a most aggravating habit. You must learn to face life seriously, Stephen. I really cannot bear the whole burden of our family affairs any longer. You must advise me: you must assume the responsibility. (1.15-17)
Lady Brit is simultaneously expecting Stephen to step up and act like a man, yet lectures him like a child. The notion that she thinks of herself as "only a woman" is pretty ridiculous, given that she's one of the most forceful and intimidating characters in the play. It may not be straight-up hypocrisy, but she definitely is contradicting her supposed belief that Stephen should be in charge. . . and not admitting that she's put her son in an impossible situation.
Oh, Adolphus Cusins will make a very good husband. After all, nobody can say a word against Greek: it stamps a man at once as an educated gentleman. And my family, thank Heaven, is not a pig-headed Tory one. We are Whigs, and believe in liberty. Let snobbish people say what they please: Barbara shall marry, not the man they like, but the man I like. (1.33)
Lady B is pretending to be the champion of liberty . . . as long as it agrees with what she wants. Again, this isn't exactly the worst kind of hypocrisy, but she's definitely saying one thing and doing something else.
STEPHEN: Mother: you have no consideration for me? For Heaven's sake either treat me as a child, as you always do, and tell me nothing at all; or tell me everything and let me take it as best I can. LADY BRITOMART: Treat you as a child! What do you mean? It is most unkind and ungrateful of you to say such a thing. You know I have never treated any of you as children. I have always made you my companions and friends, and allowed you perfect freedom to do and say whatever you liked, so long as you liked what I could approve of. (1.54-55)
Lady Brit is once again not being particularly self-aware, claiming that she never treats her children like children and has always seen them as adults—as long as she agreed with their choices. Which isn't exactly treating them like adults.
Ever since they made her a major in the Salvation Army she has developed a propensity to have her own way and order people about which quite cows me sometimes. It's not ladylike: I'm sure I don't know where she picked it up. Anyhow, Barbara shan't bully me; but still it's just as well that your father should be here before she has time to refuse to meet him or make a fuss. (1.93)
The irony here is, of course, that Lady B doesn't see that Barbara is exactly like her—and it's pretty rich that she would call anyone out for liking to have her own way.
What am I to do? I can't starve. Them Salvation lasses is dear good girls; but the better you are, the worse they likes to think you were before they rescued you. Why shouldn't they av a bit o credit, poor loves? they're worn to rags by their work. And where would they get the money to rescue us if we was to let on we're no worse than other people? You know what ladies and gentlemen are. (2.17)
Rummy is disingenuously pretending that she lies about her backstory to help the ladies of the Salvation Army, since the more dramatic stories are more compelling to the people offering donations. The irony (and hypocrisy) here lies in the fact that the Army has incentivized people to lie in order to get help and "embrace" salvation.
That's what's so unfair to us women. Your confessions is just as big lies as ours: you don't tell what you really done no more than us; but you men can tell your lies right out at the meetins and be made much of for it; while the sort o confessions we az to make az to be wispered to one lady at a time. It ain't right, spite of all their piety. (2.27)
Rummy puts her finger on the hypocrisy of the fact that the Army expects women to tell their sob stories to help the Army raise money/get converts, but they must be ashamed of those stories (and therefore whisper them). Hmm, kind of sounds like how people expect Undershaft to donate money as a display of shame for his own profession, no? If it's something worth doing, shouldn't you just own it and not be ashamed of it—and if it's wrong/something to be whispered about, shouldn't you just avoid doing it? This is the kind of hypocrisy that really gets Andrew riled up.
No: the Army is not to be bought. We want your soul, Bill; and we'll take nothing less. (2.365)
Barbara is being totally sincere, but the irony is that she's wrong—as events soon prove, the Army is to be bought—if the price is right. The problem is that he wasn't offering enough . . .
Stop. [Undershaft stops writing: they all turn to her in surprise]. Mrs. Baines: are you really going to take this money? (2.411)
Barbara now realizes that the Army is for sale, as long as enough money is involved. Even though the Salvation Army's party line is that it can't be bought and its mission runs counter to Undershaft's business, they are accepting money from Andrew because it's a lot of money.
You lie, you dirty blackguard! Snobby Price pinched it off the drum when he took up his cap. I was up here all the time an see im do it. (2.463)
Despite having said he would donate the sovereign, Bill is super annoyed to see that Snobby Price has stolen it. Rummy, however, is all too pleased to break this bad news to the man who hit her in the face for no reason.
You know he will. Don't be a hypocrite, Barbara. He will be better fed, better housed, better clothed, better behaved; and his children will be pounds heavier and bigger. That will be better than an American cloth mattress in a shelter, chopping firewood, eating bread and treacle, and being forced to kneel down from time to time to thank heaven for it: knee drill, I think you call it. It is cheap work converting starving men with a Bible in one hand and a slice of bread in the other. I will undertake to convert West Ham to Mahometanism on the same terms. Try your hand on my men: their souls are hungry because their bodies are full. (3.318)
Undershaft seems to think that it's kind of hypocritical to claim a moral high ground in converting people when you're basically bribing them with food (i.e., not exactly tempting them just on the merits of Jesus).