Even though he's the patriarch of the Undershaft factory and has been bankrolling his wife and children, Andrew Undershaft hasn't actually stepped foot in his own house for years until the day the play opens. Why, you ask? Well, the short answer is because he wanted to disinherit his own son, but the larger reason is that Lady Britomart decided he was a thoroughly immoral person. As you move through the play, you'll indeed find that Andy has some qualities and convictions that make him a lively and controversial addition to the family mix.
Even though Undershaft shares a name with a famous English church, don't be fooled—he's not the religious type. Well, in the typical sense. According to Lady Britomart, he worships a kind of "religion of wrongness," which is what made it impossible for her to keep him around:
I really cannot bear an immoral man. I am not a Pharisee, I hope; and I should not have minded his merely doing wrong things: we are none of us perfect. But your father didn't exactly do wrong things: he said them and thought them: that was what was so dreadful. He really had a sort of religion of wrongness. Just as one doesn't mind men practising immorality so long as they own that they are in the wrong by preaching morality; so I couldn't forgive Andrew for preaching immorality while he practised morality. You would all have grown up without principles, without any knowledge of right and wrong, if he had been in the house. You know, my dear, your father was a very attractive man in some ways. Children did not dislike him; and he took advantage of it to put the wickedest ideas into their heads, and make them quite unmanageable. I did not dislike him myself: very far from it; but nothing can bridge over moral disagreement. (1.67)
So, in sum: It seems that Andrew had no problem acting right, per se—it was just that what he preached was so immoral in Lady B's view that he had to be kept from his own children.
But just what is that philosophy? Well, we find out once Undershaft himself arrives on the scene and he gives us more than a mouthful about his own particular brand of "spirituality." When Barbara asks him what his religion is, he says:
My religion? Well, my dear, I am a Millionaire. That is my religion. (2.164)
Barbara disapproves, but he…sticks to his guns…about wealth being the path to all that's good and holy in the world. Later, when he's talking to Dolly, he declared the two things necessary for salvation as money and gunpowder. Surprised, Dolly asks,
Excuse me: is there any place in your religion for honor, justice, truth, love, mercy and so forth? (2.232)
To which Undershaft replies,
Yes: they are the graces and luxuries of a rich, strong, and safe life. (2.233)
So there you have it: being financially stable and/or rich allows for virtues according to Undershaft's philosophy. In fact, they can't even exist without the money. Of course, this is very different from the whole "The meek shall inherit the earth" philosophy, which is one of the hallmarks of Christianity.
Undershaft made his buckets of money by making weapons—not just for England, but for people around the world. He inherited the business from a man who was also named Andrew Undershaft, who adopted him as a foundling—an abandoned or orphaned child. According to Lady Brit, that had been the tradition in the family since the original Andrew Undershaft was born as a foundling in the parish of St. Andrew Undershaft.
Beyond the fact that he makes weapons, his family is pretty judgy about how unbiased he is about selling those arms. Patriotism doesn't get in the way of business for Andrew; he's happy to sell his arms to the highest bidder. As with his view of religion, it's not just pure self-interest; he has a philosophy of right and wrong . . . it's just different from everyone else's. When asked what the "true faith" of an armorer is, he says:
To give arms to all men who offer an honest price for them, without respect of persons or principles: to aristocrat and republican, to Nihilist and Tsar, to Capitalist and Socialist, to Protestant and Catholic, to burglar and policeman, to black man, white man and yellow man, to all sorts and conditions, all nationalities, all faiths, all follies, all causes and all crimes. (3.293)
Although Lady Britomart thinks it's only right to sell arms to good people and refuse to sell to bad people, Undershaft refuses to make that designation—though he does want "the good" to take advantage of what he's selling. When Dolly is pressing him with questions about the morality of the business, he brushes off his concerns by saying it's really not up to him how people act:
I will take an order from a good man as cheerfully as from a bad one. If you good people prefer preaching and shirking to buying my weapons and fighting the rascals, don't blame me. I can make cannons: I cannot make courage and conviction. Bah! you tire me, Euripides, with your morality mongering. (3.302)
So, according to Andrew, if the good are to keep up with the bad, they're going to need to arm up. And since Undershaft provides them with what they need to do that, he's in the clear morally, in his view.
Okay, so he makes weapons and offers up some shocking, morally questionable quotes throughout the play, but Andrew has a kind of endearingly sweet (if bewildered) quality when he first interacts with his family. He insists on calling his extremely regal and commanding wife "Biddy" and "My love," affectionate as ever despite her disdain and repeated objections to the Biddy nickname.
Also, when he first shows up to see the family after several years, his good-natured confusion about the number of children he has and who they are is oddly endearing. Normally we might not think that forgetting such key information is sweet, but he's so apologetically befuddled that we kind of want to cut him some slack. We just can't help liking the guy at least a little bit.
Well, after all, Shaw thought of him as the hero of the play, so he has to be somewhat endearing, right?