What do Christians think about this...

[MaxPowerPoker]

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it is better to pray to a false idol in a true spirit than to worship the true God in a false spirit.

I take 'false spirit' to signify a lack of devotion or sincerity. Conversely, a true spirit would entail sincere devotion.

Kierkegaard is a Christian. Is this idea unique among Christians? Does it contradict Jesus' teachings?

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This idea is not Christian. Praying to a false idol breaks the second commandment. Not a good.

Praying to the true and living God without sincere devotion... Hmm. Does that mean that you do not believe in the God you are praying to? Does it mean that you are distracted and are not praying fervently? I'd say that if it's the former then your prayer is useless. If the latter, it seems clear to me that that does not rise to the level of idolatry.