Despite largely approving of his politics, my mother could never vote for Ted Kennedy, for reasons that boiled down to one word: Chappaquiddick. Her opinion of him as a politician collapsed under the weight of one tragic event that, she felt, defined him as a man.

While that’s an extreme example, it underscores a reality involving all manner of celebrities — politicians, yes, but also entertainers and athletes — raising the question of whether it’s possible to separate public accomplishments from private actions, or when distaste for the personal wholly invalidates the professional.

To those weaned on Bill Cosby’s standup albums and TV work, the sexual-assault allegations leveled against him follow a similar trajectory to those aimed at other luminaries of his era — from Woody Allen’s complicated personal life tainting enjoyment of his movies to reconciling Roman Polanski’s rape of an underage girl with appreciation for the director’s masterpiece “Chinatown.”

Not all these situations, obviously, are equal, nor are moral dilemmas confined to potentially criminal or unsavory behavior. In these polarized times, it’s become common for people to vow that they will shun a performer’s work because of his or her political leanings and affiliations. And while those who actually follow through on ideologically motivated boycotts represent the fringes, to borrow from the Dixie Chicks, there’s clearly a “Shut up and sing” mentality — whether that’s Alec Baldwin and Sean Penn on the left or Jon Voight and Kelsey Grammer on the right, saddling certain stars with extra baggage.

Activists have become especially adept at quickly mobilizing in response to outrageous statements or behavior, with social media not only providing a rallying point, but also serving as a new platform by which to alienate consumers by sticking one’s foot in one’s mouth. An arena in which one must seek to condense complex issues to 140 characters has come to contain especially fertile soil for missteps, as just evidenced by Fox mogul Rupert Murdoch’s observation about the racial composition of Egyptians, while defending the casting in “Exodus: Gods and Kings.”

Having erred in the past by ignoring or whitewashing the private lives of public figures, the media now have largely swung in the opposite direction, eagerly pouncing on transgressions large and small. The hunger for ratings and traffic provides a special incentive to play up media figures when they cross over into the political realm, from the biblical scholarship of “Duck Dynasty” patriarch Phil Robertson to ESPN baseball analyst Curt Schilling tweeting his skepticism about Darwin’s theory of evolution.

The latest “American Masters” documentary, “Bing Crosby Rediscovered,” would have thus felt incomplete had it not at least acknowledged accusations of abusiveness raised by some of his children, which has become a part of the multifaceted star’s legacy, along with “White Christmas” and “Going My Way.”

Determining at what point the drumbeat of scandal eclipses a lifetime of achievement remains a gray area, as I unexpectedly had to contemplate recently while writing a review of a children’s program. The tone and exaggerated childhood memories felt reminiscent of Cosby’s “Fat Albert” and related characters, but the comic has become so toxic, it was awkward to reference him without a disclaimer. Ultimately, the comparison didn’t make the cut.

A broader perspective, though, reveals an uncomfortable truth: that we have seldom relied on saints and choirboys to lead or entertain us. What’s often left, then, is personal bargaining and rationalization, such as (in Allen’s case) continuing to embrace “Sleeper” and “Annie Hall,” while deciding “Manhattan” strikes a little too closely to the filmmaker’s personal history, given the protagonist’s relationship with a 17-year-old girl.

Not that the routines aren’t funny, or the movies aren’t still great. But in this day and age, it sometimes seems the only thing more ill-advised than having childhood heroes is knowing too much about them.