While not exactly a denomination, the famous baseball-player-turned-pastor, Billy Sunday, is probably most associated with the evils of "theater, cards, and dance." His influence on Fundamentalists, Baptists, and Evangelicals of all stripes is legendary.
Sunday's popularity influenced thousands (if not millions) in the United States in the early 1900s. His brand of fundamentalism led directly to many of the beliefs you see. Early in the Century, this type of preaching was de riguer. Its influence, however shall we say, has since waned. (I for one, do not mourn its passing.) That said, for those who grew up in it, the tenants still hold.
In his estimation, the primary issue with cards is that they do lead to gambling. His takes inspriation from Galatians, in which it says "Do not be decieved, God is not mocked - for that which a man soweth, so shall he reap."
He preaches as follows: (The full text is here)
You sow bridge whist and auction pitch and five hundred in the home and you reap a crop of gamblers. You sow the dance and the ballroom and you reap a crop of brothels. You sow saloons and you reap a harvest of drunkards.
You must want a lot of prostitutes or you wouldn't sow dances; you must want a lot of vomiting, puking drunkards or you wouldn't sow saloons, and you must want a bunch of gamblers or you wouldn't play cards in your homes.
If you have any cards in your home, you had better throw them in the furnace when you get back there or else throw your Bibles in the furnace. The two won't mix. Oh, you need not gasp! I am handing it to you straight! There is no use having Bibles around your house if you are going to make a joke of His Word by playing bridge.
(As you can tell, he gets emotional about it.) Perhaps his most damning indictment is this:
Many a boy is inveigled into a gambling room and listens to the roulette wheel ¥ the faro bank and keno and listens to the ribaldry and the jest and the blasphemy, and he is reminded of home. What a wonderful heritage to bequeath to a boy! To have him go into a hellhole like that and have it remind him of home! Men who have been spending their funds and lives to ferret those things out tell us that nine-tenths of the gamblers are taught in their homes by their mothers, or eighty per cent of them first learned gambling in the homes of professing Christian people.
When I talk to you about card playing in your home, I am trying to pound through your head that every pack of cards is but another steppingstone to Hell. I think the old painted hag or the broken down roue, hanging around the tables at Monte Carlo, or a down-and-out card shark bucking a crooked game in a gambling joint at three o'clock in the morning a sight more respectable than the church people or the professed Christian who permits card playing in his home.
"You take that picture back and give it to my mother, and tell her 'Damn her!' I never want to see her. She taught me to play cards and I killed a man at a gambling table and am serving fifteen years to pay for it. Now she has the audacity to send me her picture after she pushed me behind the prison bars," so said a condemned boy.
I say it may not injure you, but it is damning others. Many a boy leaves home and goes to board in some miserable, no-account church-member family. The first night they draw out a card table and take out a deck of cards and say: "Won't you play a game with us?"