In contrast, other prominent Mormons have thanked Romney for presenting a positive image of the church.
J.W. Marriott, head of the Marriott hotel chain and a family friend of the candidate, told Romney's church congregation in Wolfeboro, N.H., that Romney's presidential run has been good for the Utah-based faith.
"There has never been as much positive attention to the church, thanks to the wonderful campaign of Mitt Romney and his family," Marriott said, according to news reports.
Reid, the highest-ranking Mormon in elected office in America, noted on Friday a recent opinion piece published in the Huffington Post by Gregory A. Prince, co-author of "David O. McKay and the Rise of Modern Mormonism."
Prince, who said he backed Romney in his Massachusetts gubernatorial bid and in his 2008 run for president, railed against GOP nominee after a surreptitiously recorded video emerged in which the candidate said 47 percent of Americans play the victim card and believe they are entitled to government handouts.
"Judge Mitt Romney as you will, and vote for or against him as you will; but do not judge Mormonism on the basis of the Mitt Romney that was unveiled to the public this week," Prince wrote. "He is not the face of Mormonism."
Reid, on the conference call, said, "I agree with him."
"He said that Romney has sullied the religion that he, Prince and Romney share," Reid said. "And he's so disappointed that in his words, 'It's a good religion and he's hiding from it.' "
Reid took to the Senate floor last week to castigate Romney for his "47 percent" remarks and has frequently criticized the Republican for not releasing more than two years of tax returns claiming at one point that Romney had not paid taxes in some years.
Romney's campaign says the candidate has not paid less than an effective tax rate of 13 percent in the past decade.
Rep. Jason Chaffetz, a Utah Republican who is also Mormon, said Reid knows well that the LDS Church preaches for members of all political stripes to be engaged in the public square but that he shouldn't be trying to use Romney's faith against him.
"Shame on them," Chaffetz said, referring to Reid and Prince. "Harry Reid seems to be making this way too personal and consequently throwing the religion under the bus for his own personal gain. That's not where anyone should be going with this. He's taking this two steps too far."
Jana Riess, an author and blogger, said in some ways, this Reid vs. Romney debate could be good for the faith because it shows that Mormons aren't monolithic in political persuasion.
"They're arguing about which face of Mormonism to show, but the fact is there are many different facets to who Mormons are," she says. "In
the end, that is a positive outcome of this type of public squabbling."
Thomas Wright, chairman of the Utah Republican Party whose father, the late William Robert Wright, co-wrote the McKay book with Prince, said it's likely his dad would be disappointed in what Prince and Reid are saying.
"It's unfortunate when the dialogue turns to someone's religion when they're running for president," Wright said. "I've not run across one Mormon who thinks that Mitt Romney is not a good face for Mormons and for two liberal Democrats to use that ploy to try to convince Mormons and Democrats to vote against Romney is disappointing and sad."