Judge the situation and act accordingly. There's no way absolutes can be drawn up for something like this, as most other people in here have touched upon.
Interestingly though, second chances on a public scale, such as the population forgiving a public figure for some sort of offensive comment, can often be sorted into absolutes. We generally abandon and crucify a person for harmful sexual misconduct, especially in regards to underage sex. R. Kelly as a figure has never recovered from the video of him 'allegedly' pissing on a minor, for instance. Naturally, people still go wild to his music, but he's been largely abandoned since 2002/2003. Though given that he was illegally married to Aaliyah when she was 16 and he was approaching 30, people should have seen it coming.
Racism from public figures tends to have a 50/50 chance of ruining their career, depending on the comments made and how angry white society gets at the figure. I'll also throw anti-semitism into this point just to be concise. Second chances are sometimes available to the figure, but they're still very limited and the figure is rightfully treated with contempt for the rest of their career, should they even have one.
Paula Deen might as well be dead, she'll never get another chance from the public. Michael Richards of Cosmo Kramer fame also might as well be dead. Mel Gibson has sort-of gotten a second chance over the years, but he'll always be seen as suspect. If we dig back into the '90s, there was Ted Danson of Cheers fame doing blackface. Given that he fronted CSI for a few years, I'd say he got a second chance over time. Whether or not racism/anti-semitism is something that should deny someone a second chance is not something I'm debating. I'm just showing that the public has been relatively cautious with giving out second chances in regards to that subject.
Drugs & alcohol... well, that is also a 50/50 subject. But the second chances come more from within the public figure's chosen field rather than from the public. Robert Downey, Jr for example is bigger than he's ever been and he quite famously lost his career to substance addiction a while back. But somehow he was able to land Iron Man and you know the rest. I think people tend to be shocked rather than condemning when it comes to public figures and addiction.
I don't really know the point I'm making here, to be honest. I think I'm just illustrating how we've been relatively incapable of maintaining absolutes. Second chances may be fickle, or a way of not accepting true responsibility for one's actions, but as I said in the very beginning, we have to judge the situation and act accordingly.