California can probably be explained by demographics changes. While the Bay Area had always been relatively liberal in the modern party system, Southern California began trending towards Democrats as the Hispanic population increased (from 19.6% to 25.6% of the population between 1980 and 1990). Southern California had originally been a Republican stronghold (and parts of it such as Orange County still are, more or less) owing to the strong aerospace defense industry in the area.
The change may also have been obfuscated in part owing to the election campaigns of Ronald Reagan (a native son and former Governor) and George H.W. Bush (who won in a relative landslide nationally). Notably, by the '80s, Republicans no longer controlled the majority of California's House delegation. Therefore, it's likely that this switch from California being a solid red to solid blue state could've happened much sooner had it not been for the blowout elections in the '80s for Republicans.
This may also explain New England's sudden switch as well. The Southern Strategy was already well under way by Clinton's time; it may have required a more competitive election to see the realignment come into play.
I can only speak to the California piece, unfortunately, but generally speaking, the 1991-1992 recession and accompanying drop in real estate prices/home construction hit the state pretty hard. Unemployment rose from a low of 5.2% in 1989 to 9.4% in 1992. According to the LA Times year-end wrap up, real estate volume declined by 3% in 1992 and was the lowest sales rate in seven years. In addition, Southern California's traditional economic engine - aerospace - experienced negative fallout from the end of the Cold War and subsequent defense cuts.
Significantly, minority voters were not the force they would become. In 1992, just 21% of election day voters were minorities and only 51% of Latinos that year voted for Clinton. Reagan had historically performed fairly well with Latinos and most writing I can find from the time indicates conventional wisdom believed they would continue to split evenly between the parties.
So for 1992, I think it's fair to say the recession and its impact on California's housing market drove voters away from Bush and towards Clinton. However, post 1992, the story shifts.
In 1994, then-candidate (and soon-to-be governor) Pete Wilson (R) backed Prop. 187. This now-infamous law (also known as the Save Our State initiative) called the state to screen and deny state services like education and health care to illegal aliens. Unsurprisingly, the Latino community saw the proposition as a discriminatory attack on their increasing numbers and protested the bill. Though the prop was spearheaded by Wilson and the Republican leadership, it's worth noting that Sen. Dianne Feinstein (D), running for re-election, also supported tough-on-immigration policies. The prop passed easily 59-41, though three days after the election, a state judge issued an injuction against its enforcement. The law spent several years in court before eventually Gov. Gray Davis (D), elected in 1998, withdrew the government's support effectively killing the bill.
By 1996, the Latino community swung hard to the Democratic side, with 76% supporting Clinton. By then, only 9% of Latinos identified as Republicans and their participation in elections was growing. More than 660,000 additional Latinos were eligible to vote in CA in 1996, out of a total state vote count of 10-11 million. While 1996 is a bit of an anomaly, with a surging economy and Clinton's personal popularity still quite high, the partisan split persisted into 2000. Gore captured 73%, leaving Bush with 25% (according to the William Velazquez Institute's exit polling).
TLDR: In 1992, CA supported Clinton b/c of the recession/unemployment but by 1996, backlash to anti-illegal immigration policies created strong and growing Latino support to Democrats generally.
Sources - mostly LA Times articles from 1996 and 1992. Wikipedia for background on prop 187. I'm happy to provide precise sources as needed.
Edit-Davis was elected in 1998, not 1996 as previously stated and Wilson was only a candidate in '94. Thanks for the correction.
What's with all the censorship in this thread? The removed comments don't appear controversial, hostile, or inherently wrong.