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Re:Iceland to build first temple to Norse gods since Viking age by VLM on Tuesday February 03, 2015 @11:05AM (#8991078)
Freemasonry? I knows it doesn't exactly fit your proposed requirements, but its not totally a wrong answer?

If you're willing to twist the list of "good parts" possibly into an unrecognizable controversial form, there's always prosperity gospel. Most people might not think they're selecting the good parts, but the PG participants obviously disagree.

Another interesting area research along the lines you're discussing would be Buddhism in general and specifically the somewhat heretical writings of Stephan Batchelor.

Re:Iceland to build first temple to Norse gods since Viking age by maxerickson on Tuesday February 03, 2015 @03:30PM (#8993126)
Masons carefully state that that they aren't a worship group but demand that you acknowledge a supreme being to become a member. So they sort of reject the rituals and do not avoid the god question.

(for example: http://www.wisc-freemasonry.org/basics-of-freemasonry/qualif... )