The interesting thing is Merriam-Webster defines plaster saint simply as:
a person without human failings.
I sifted through Google Books, and this is the meaning you find in book after book after book. When it is explained why someone is not a plaster saint, the reason is that the person is less than saintly, misbehaves, has passions, struggles with temptation, very much unlike the other-worldly, beatific, ideal represented by a plaster saint, or the lifeless object itself.
It’s not hard to imagine how plaster saint could come to mean hypocrite: real humans are flawed; if you look like a plaster saint you must be faking it. Sarcasm could have played a role here too. However Bernard Shaw’s quote is highly atypical. Annie Edwards’ A Plaster Saint (1899) is the only other instance I found of plaster saint used sarcastically in this way.
Plaster saint in the Merriam-Webster sense appears in scores of books though. Merriam-Webster says the first known use is in 1890. So it’s likely Kipling’s Tommy, quoted by the OP, and first published that year under the title The Queen’s Uniform (The Kipling Society). Here Kipling has the proverbial British soldier Tommy Atkins criticise the British public, who sees the common soldier sometimes as a hero, sometimes as a ruffian (my emphasis throughout):
[…] Yes, makin’ mock o’ uniforms that guard you while you sleep
Is cheaper than them uniforms, an’ they’re starvation cheap.
An’ hustlin’ drunken soldiers when they’re goin’ large a bit
Is five times better business than paradin’ in full kit.
Then it’s Tommy this, an’ Tommy that, an’ Tommy, ’ow’s yer soul?
But it’s “Thin red line of ’eroes” when the drums begin to roll
The drums begin to roll, my boys, the drums begin to roll,
O it's “Thin red line of ’eroes,” when the drums begin to roll.
We aren’t no thin red ’eroes, nor we aren’t no blackguards too,
But single men in barricks, most remarkable like you;
An’ if sometimes our conduck isn’t all your fancy paints,
Why, single men in barricks don’t grow into plaster saints […]
Rudyard Kipling, Tommy aka The Queen’s Uniform (1890), (more info in Kipling Society) and full poem here
The following give a more explicit description of what a plaster saint is not:
Henry Morgan the Buccaneer was no “plaster saint”. His weaknesses, his follies, his errors are writ large on his record. He was rash, impulsive, reckless of speech, and oftentimes unscrupulous in action. He was a good hater and a firm friend.
The Transactions of the Honourable Society of Cymmrodorion, 1889, p. 41.
A study of his career will probably make us like him better, for we shall find that he was a man with very human virtues and failings, not a preposterous plaster saint.
William Alfred Hirst, Walks about London, Henry Holt, 1900, p. 80.
Sometimes the plaster saint is implicitly presented as something good:
“Look here, Elizabeth,” she said desperately, “have done with all this nonsense, for heaven's sake, and take your husband as you find him. He is no plaster saint, but neither are you, or any of us for that matter.”
Kate Horn, Ships of Desire, Cassel and Company, 1909, p. 317.
Sometimes people cultivate a plaster-saint image of important persons:
In short, she [Rose Parks] is on her way to becoming the secular version of a plaster saint. It is a fate that has already befallen Martin Luther King, who is so venerated it is politically incorrect even to acknowledge his human failings, like his womanising and his plagiarism.
“American trouble-makers,” The Economist Year Book, 1992 in Review, The Economist Books, 1993, p. 292.
the Trustees were aware of the existence of letters by Einstein, some of them since published, 15 others to be published later, that conflict with the “plaster saint” image they wished to preserve
John Stachel, Eistein from B to Z, Birkhäuser, 2002, p. 99.
Several strategies combine to defuse the image of Lincoln as a plaster saint. […] He may have contracted syphilis as a young man. […] Vidal’s very human Lincoln knows the art of the political deal.
Susan Baker, Curtis S. Gibson, Gore Vidal: A Critical Companion, Greenwood Press, 1997, p. 88.
Often we get the notion that a plaster saint is someone we wouldn’t like that much. In this case Ernie, a young girl, has a “mercurial temperament”, but is urged by her friends to beat another girl, this one perhaps a plaster saint by nature or conviction, at winning a prize for “the pupil whose general average in attendance, conduct, and scholarship should be the highest.” She says:
”All right,” promised Ernie, with a weary little sigh. “I don't mind the studying so much; but I must confess I'm tired of being a plaster saint!”
Alice Calhoun Haines, The Luck of the Dudley Grahams, Henry Holt, 1907, p. 173. (Full book available here.)
And even real saints are no plaster saints
Do not for one moment picture him [Saint John Bosco] as a little monster of perfection, with no personality, no reactions, anaemic as a plaster saint. The retiring, timid, peaceable, passive one was not John, but his brother Joseph—an intelligent, hardworking boy, marked from the beginning with mark of those who will never go above or below the level of a decent obscurity. But John was a different matter […]
Henry Ghéon, The Secret of Saint John Bosco, Tradibooks, 1944, p. 21.
As to whether plaster saint was borrowed from another language I found no evidence of. The literal equivalents plâtre saint or saint de plâtre in French, santo de yesso in Spanish, and santo de gesso in Portuguese, mean the object only. Petit saint (little saint) is used ironically to refer to a person hypocritically affecting virtue, and has been in use since the early 1800s. Ce n’est pas un (petit) saint (he/she is no (little) saint) sounds very much like the English phrase and has been around since the early 1800s too, but means they’re dishonest. My hunch, for all it’s worth, is that the phrase as used in the examples above is transparent and suggestive enough for English speakers to have coined it without outside help.