FWIW, maybe nothing, I sort of reject the "don't judge someone by their worst moment" theory being applicable here. (Not judging those who do, just want to share this perspective.) To me, if Duran had said something like this after the infamous "give-up" play, while he was apparently suffering from a lot of anxiety, depression, and stress, that would be a "worst moment" kind of context: he wasn't himself or at his best and that can lead to out of character moments that, yes, are moments that don't necessarily show someone's true character. If he'd said this slur the day after that play, I'd understand the application of the aphorism here.
But... that is not at all what happened here. He had that word so ready on his tongue that he tossed it out during an off-hand remark to a stranger. That indicates that he does not understand its significance, vileness, nor inappropriateness. The context of the moment does absolutely nothing to protect him, for me. A professional baseball player being heckeld I believe deserves no special protection or forgiveness in his retaliation. Most people would be fired if they were heard talking to a paying customer like that, much less on camera. I'm perfectly happy to judge someone by their "worst moment" when it leaps out of them unprompted, in public.
That's not to say Duran is dead to me or can't make it right. I'm not calling for him to be cut or traded or whatever; these guys are human and a lot of them are not very good dudes. This is not breaking news. It appears that Duran is one of those dudes, which is disappointing but shouldn't be surprising. If you let the fact that some players are not good people bother you, you realistically can't enjoy professional sport, almost at all. So we constantly have to decide where to draw the line for ourselves. I wouldn't get a beer with Duran, but I'm not gonna change the channel when he comes up. I've watched worse dudes.
I can imagine getting over it and moving on. That said, the kind of contrition I would need to see in order to "forgive" is long-term change in behavior and attitude. Apologizing and taking responsibility is a good start, but anything he says this week doesn't count much for me; it's spin and PR and mitigation right now. To show true contrition would ideally go beyond mere words and reach meaningful actions. If he does that, I can imagine forgiving and forgetting, but I'll need to see it for a while before I'm going to believe it. Show me Duran volunteering in the off-season, sitting down with community leaders to discuss getting that word out of baseball clubhouses for good (because realistically we all know it is not uncommon there), writing a check to BAGLY or a similar local org, etc. That's the kind of stuff that puts this properly behind him, at least in my eyes.
He's shown some fairly impressive ability to be introspective and vulnerable, so I have hope that he might take his penance seriously and re-earn credibility. It will take time, and work, but, he's done that in baseball in the past, maybe he can do it here too. I hope so. It's really the most disappointing thing that's happened around the team in years, for me.