On Apologies
I think the point of making an apology is misunderstood by many people. I see a lot of takes about apology that treat it as an act of total abasement. You're supposed to fully and freely admit your wrongdoing, commit to specific changes you're going to make, offer full compensation for any harm, etc. And then it is still left up to the other party's decision whether or not they choose to accept the apology.
In my experience, this is not really how apologies work, and these expectations are unrealistic.
Before circling back to apologies though, let's talk about communities. People live as part of various formal and informal communities. (I'm not just talking about "official" communities here; I think my thoughts apply equally to a friend group, an extended family, or whatever.) The thing about communities is they only work when everyone in the community is committed to getting along. A conflict between community members threatens the whole community. If two people can't be in the same room together, you don't have much choice other than to expel one or both of them from the group. However, a community in the habit of regularly expelling members will not last very long. Each expulsion also runs the risk of splitting the community in half along some fault line. If enough people side with the person being expelled, the community can just fracture.
Judicious expulsion of troublesome members is necessary to having a functional community. But you have to handle it carefully, and you can't treat it as the primary tool of community management.
With all the above in mind - the point of an apology, as I see it, is to restore normal relations within a community. An apology does typically involve an admission of guilt, as well as some form of compensation. But this is directed at a particular end - restoration of the relationship. It's not just something you do because you feel bad about it. And it doesn't have to be a total capitulation. Just as two countries can sign a treaty to end a war while still disagreeing substantially, two people can choose to reconcile while still holding various grudges and believing themselves to be in the right.
There is often pressure on both parties in a conflict to work it out. That's because everyone in the community benefits if the two parties are able to settle their differences and move on. The exact nature of the settlement is often less important than just getting things back to normal. This is also why there can be a lot of social pressure to accept an apology once it's offered, even one that doesn't feel 100% sincere, or doesn't fully compensate for whatever offense was made. Compensation is offered to prove seriousness and bring the aggrieved party to the table, not necessarily to set everything 100% right. Importantly, the audience for the apology is not just the aggrieved party but also the community as a whole. The idea is to be reasonable enough that, if the community has to pick one side to expel, they'll pick the other side. When an apology is offered to you, it's best to see it as a negotiating position rather than judging it against a platonic ideal.
I think it's harmful and destructive to insist on "perfect" apologies. People *almost always* believe that their behavior was justified, understandable, reasonable, etc. After all, if they didn't believe that, they wouldn't have done it. Truly sincere apologies will never be common, no matter what you do. If you make true, genuine sincerity your requirement to accept an apology, you are essentially placing the value of your shared community at zero, and are committing yourself to blowing up every community you're a part of. The nature of communal life is learning to let go of conflicts. Or at least, learning to let conflicts subside to the point you can be around each other and be civil.
This doesn't mean you have to accept every apology. I definitely think there are offenses that should not be forgiven. But refusing to accept an apology ought to be understood as the opening of impeachment proceedings. You are implicitly telling the community they have to choose between you or the other party. If that's what you want, then go for it. But you ought to understand that's what you are doing. And you ought to be aware that others in the community are within their rights to decide the other party is more valuable to have around than you are, regardless of any particular offense.
(I'll pause here to note that certain types of offenses, such as sexual harassment, are deeply corrosive to community life, and ought not be tolerated. This is not because these offensives are ontologically unforgivable, but rather because systematically punishing and removing offenders will benefit the community as a whole. It is up to each community how exactly they want to draw these lines, but such lines ought to be drawn and made clear. In these cases, an apology is not usually relevant at all, and punishment or expulsion should simply be carried out as a matter of formal or informal policy.)
This perspective also offers some insight into the strange phenomenon of the online apology. The trope here is that some figure does something offensive, gets a lot of blowback, and then releases some sort of statement, video, or whatever that apologizes for their behavior.
My experience is that this tends to feel rather unsatisfying. A big part of that is that there's usually not any specific aggrieved party available to accept the apology. Internet outrage is fundamentally diffused and decentralized without obvious leadership. So random posters are free to simply demand that the offender "do better."
This doesn't make online apologies totally pointless. At their most effective, they reassure fans that it's okay for them to continue to associate with and follow an online figure. But if you are a fan reading an apology, you ought to keep in mind that each individual has to decide on their own if the apology is sufficient. There is no possible apology that will satisfy every single person, and there is no coordination mechanism in place to get everyone on the same page to agree to accept an apology. The opposite happens actually, because the incentives point everyone in the direction of performatively rejecting the apology.
I think that approaching apologies as a negotiated end to a conflict is much healthier than treating them like they're supposed to spring true and clear from a sincerely contrite mind. Conflict is normal, and we need tools to resolve conflict. Apology is an important tool in the toolbox. An apology doesn't need to be 100% sincere and doesn't need to perfectly compensate for every perceived harm. The truly important message of the apology is that the other person cares enough about their relationship with you and your shared community to make an effort at mending things.