The quote is a paraphrase of statements Carter made to a Star Tribune reporter as part of a Nov. 11, 2005, article promoting his book "Our Endangered Values." The statement appears without quotation marks in that Star-Tribune article, and the book in question does not include that sentence.
The origin of this statement is a Nov. 11, 2005, article in the Star Tribune. At the time, Carter was promoting his recently published book "Our Endangered Values: America's Moral Crisis." A Tribune journalist interviewed Carter for the story, paraphrasing his book's broader point (emphasis ours):
Donning the mantle of alarmed prophet in "Our Endangered Values: America's Moral Crisis," the 81-year-old former president is promoting the book, which implores Americans to reject the fundamentalist values that now marble domestic and foreign policy.
Referring often to his own brand of evangelical Christianity, Carter said he could remain quiet no more about the Christian far right and its influence on government. Evangelical Christianity has been hijacked, he said, by people who would give Jesus himself the boot if he knocked on their door.
This is not a direct quote from Carter. If it was, it would be contained in quotes. This is, instead, the reporter’s colorful paraphrase of the views contained in Carter’s book.
According to its publisher Simon and Schuster, Carter's book "offers a passionate defense of separation of church and state, warning that fundamentalists are deliberately blurring the lines between politics and religion." This book, importantly, does not contain the statement about evangelicals theoretically giving Jesus "the boot."
Because the words in the meme stem from a newspaper reporter and not Carter, and because there is no documented evidence of Carter saying or writing the words, Snopes concludes that this quote has been falsely attributed to Jimmy Carter.