At Politico, Michael Kruse and Manu Raju write:
The most surprising thing about the independent Vermont senator’s surprisingly successful campaign so far is not that he’s doing it as a self-described democratic socialist. It’s that he’s seeking the nomination of a party he caucuses with in the Senate but is not a part of, isn’t a registered member of and has never been a registered member of—a party he’s spent his 40-year career beating at the polls and battering in the press.
He started as a politician in the 1970s as a perennial protest candidate with the anti-Vietnam War Liberty Union Party, offering voters an alternative to the two major parties, which he considered ineffective and equally beholden to corporate lords.
To become mayor of Burlington in 1981, he ousted a veteran centrist Democrat. To build power, his progressive allies in subsequent elections wrested away city council seats, relegating local Democrats to diminished, third-party status. In a series of statewide races in the late ’80s and into the early ’90s, he outdid even that—getting Democrats to all but wave a white flag when he ran.
He has never before chosen to run in a Democratic primary, but here he is, challenging Hillary Clinton—and doing it as an independent, technically permissible but highly unusual. How he’s trying to do this is how he always has—a calculated alchemy of outsider edge and insider smarts, provocation plus pragmatism, all learned and honed over what’s become a unique career in modern American politics.
As Timothy Noah pointed out in Politico a couple of weeks ago, Trump's connection to the GOP is almost as tenuous:
In 1999, Trump quit the Republican Party, saying “I just believe the Republicans are just too crazy right.” Trump was then conferring with political consultant Roger Stone about a possible presidential run as a candidate of the Reform Party, the political organization founded by his fellow billionaire Ross Perot.
In 2001, Trump quit the Reform Party to register as a Democrat. “It just seems that the economy does better under Democrats,” he told CNN’s Wolf Blitzer in 2004. The Clintons attended Trump’s Palm Beach wedding to former model Melania Knaus in 2005. The following year Trump gave $26,000 to the House and Senate campaign committees.
By the late aughts, though, Trump’s political giving had started shifting back to the GOP, and in 2009 Trump registered again as a Republican. Two years later he registered as an independent while contemplating a third-party bid.
