Despite their decades-long record of shaking hands with tyrants whose nations posed an existential threat to the United States, when President Obama shook the hand of one who did not Republicans nevertheless took to the fainting couch. The image of Obama's brief handshake with Cuba's Raul Castro prior to his address at the memorial service for Nelson Mandela was more than John McCain could take. "Neville Chamberlain shook hands with Hitler," McCain analogized after asking:

"Why should you shake hands with somebody who's keeping Americans in prison? I mean, what's the point?"

That's an odd question for the self-proclaimed "foot soldier in the Reagan revolution" to pose. After all, to secure the release of Americans held by Iranian proxies in Lebanon, in 1986 President Ronald Reagan sent the mullahs in Tehran a cake, a Bible and American weapons.
The Iran-Contra scandal, as you'll recall, almost laid waste to the Reagan presidency. Desperate to free U.S. hostages held by Iranian proxies in Lebanon, President Reagan provided weapons Tehran badly needed in its long war with Saddam Hussein (who, of course, was backed by the United States). In a clumsy and illegal attempt to skirt U.S. law, the proceeds of those sales were then funneled to the contras fighting the Sandinistas in Nicaragua. And as the New York Times recalled, Reagan's fiasco started with an emissary bearing gifts from the Gipper himself:

A retired Central Intelligence Agency official has confirmed to the Senate Intelligence Committee that on the secret mission to Teheran last May, Robert C. McFarlane and his party carried a Bible with a handwritten verse from President Reagan for Iranian leaders.
According to a person who has read the committee's draft report, the retired C.I.A. official, George W. Cave, an Iran expert who was part of the mission, said the group had 10 falsified passports, believed to be Irish, and a key-shaped cake to symbolize the anticipated ''opening'' to Iran.

(Among the Iranians involved in Ronald Reagan's outreach to the Ayatollah were two men who names might sound familiar to Americans today. One was Mir-Hossain Mousavi, the former Prime Minister turned reform presidential candidate in 2009. The other was the current president, Hassan Rouhani.)
The rest, as they say, is history. After the revelations regarding his trip to Tehran and the Iran-Contra scheme, a disgraced McFarlane attempted suicide. (That would be the same Bud McFarlane whose endorsement Newt Gingrich touted during a 2011 GOP debate.) After his initial denials, President Reagan was forced to address the nation on March 4, 1987 and acknowledge he indeed swapped arms for hostages (video here):

"A few months ago I told the American people I did not trade arms for hostages. My heart and my best intentions still tell me that's true, but the facts and the evidence tell me it is not. As the Tower board reported, what began as a strategic opening to Iran deteriorated, in its implementation, into trading arms for hostages."

(For more background, read the Reagan diaries, starting with the part in which he admits in 1986, "I agreed to sell TOWs to Iran." TOW is an acronym for "Tube-launched Optically-tracked Wire-guided missile," one of the weapons Reagan sold to the Iranians by the hundreds to destroy the tanks and helicopters of his ally, Saddam Hussein.)
Of course, the sad saga didn't end there. Then Lt. Colonel and now Fox News commentator Oliver North saw his Iran-Contra conviction overturned by an appellate court led by faithful Republican partisan and later Iraq WMD commissioner Laurence Silberman. And in December 1992, outgoing President George H.W. Bush provided Christmas pardons to Defense Secretary Caspar Weinberger and five other Iran-Contra scandal figures. Among them were John Poindexter and Elliott Abrams, men who eight years later reprised their roles in the administration of George W. Bush. (As it turns out, Abrams - one of the people who brought you the Iraq War - also served as an adviser for Mitt Romney during the 2012 presidential campaign. In that capacity, he argued that Congress should give the President the authorization to use force against Iran for a preventive war to destroy Tehran's nuclear program.)
For his part, John McCain was troubled, but not too troubled, by Reagan's Iran-Contra fiasco. As the New York Times recounted in 2000, McCain "defended Ronald Reagan during the Iran-contra inquiry." About that inquiry, McCain said in May 1987, "I detect no electricity in the air and no surge of anticipation." But after it was all over, as a March 2006 profile in Current Biography revealed, John McCain showed empathy for the perpetrators of Iran-Contra:

He criticized the administration's handling of the Iran-Contra affair (in which officials had illegally diverted to the Contras money from the sale of arms to Iran), though he blamed both Congress and the White House for failing to work more closely on a coordinated foreign policy, and he empathized with his fellow Vietnam veteran Oliver North, a central figure in the scandal. "Some of these people like Ollie North," he explained to Michael Killian for the Chicago Tribune (July 29, 1987), "who saw their comrades and friends spill blood and die on the battlefields in a war that they believe the politicians wouldn't let them win--I think that leads to a mind-set which could rationalize deviating from the established rules and regulations."

As it turned out, rationalize John McCain could--and did. When President George W. Bush used a 2008 speech to the Israeli Knesset to issue a none-too-thinly veiled charge of appeasement against then candidate Barack Obama, GOP presidential nominee McCain heartily agreed. As the New York Times detailed:

"Yes, there have been appeasers in the past, and the president is exactly right, and one of them is Neville Chamberlain," Mr. McCain told reporters on his campaign bus after a speech in Columbus, Ohio. "I believe that it's not an accident that our hostages came home from Iran when President Reagan was president of the United States. He didn't sit down in a negotiation with the religious extremists in Iran, he made it very clear that those hostages were coming home."

Of course, in 1986 the Reagan administration did sit down in a negotiation with the religious extremists in Iran. And one cake, one Bible two Colt pistols and millions of dollars-worth of U.S. weapons later--all part of Ronald Reagan's outstretched hand to Ayatollah Khomeini, most of America's hostages remained firmly in Hezbollah's control in the Bekaa Valley in Lebanon.
As John McCain might put it, "Why should you shake hands with somebody who's keeping Americans in prison? I mean, what's the point?"
After all, it's not like Reagan and Khomeini were just bumping into each other at a state funeral.