Why didn’t Putin’s past as a KGB agent destroy his post-USSR political career?

[FEMA Camp Administrator]

"Right-wing Russians" is sort of a nebulous concept; while there were attempts to formulate ideologically programmatic parties, these of course fell by the wayside, and the center-right in any case could be characterized as "liberal" in Russia. Privatization aside, liberals were an opposition force even in the 1990s ("Yabloko" being the big-name party there). If you mean "conservative" Russians, they probably had no reason to care that a man had been in the security services (let alone in as innocuous a position as Putin, described above).

I can't contribute much to Cassius' big picture view, but it's also worth noting that his first foray into politics was local, as he was recruited into the administration of St. Petersburg's first democratically-elected mayor, Anatoly Sobchak. After Sobchak lost the first for re-election, Putin then transferred to Moscow owing to the favor of a St. Petersburg-based official (as I recall) and then proceeded to hold a number of appointed positions (including head of the FSB) before becoming prime minister then president. So it's not like he was out there in 1994 trying to run for state senate and someone was like "Hey, weren't you part of the KGB!?" He was a bureaucrat handling bureaucratic responsibilities.

It's probably also worth noting, as described in other ways by the above posters, that the collapse of the Soviet Union was not necessarily a rejection of the Soviet system by Russians themselves. The breakup began in the Baltics and, if I recall correctly, Yeltsin launched Russia's secession from the Union based on the idea that Russia should no longer support for other republics (my grasp of that period is shaky). You weren't persona non grata for having "collaborated" with the regime--this wasn't post-Vichy France.