Meaningful apologies can be easily found via the search engine of your choice, "How to apologize" brings up lots of hits. The thing they all have in common though is an acknowledgement (in one form or another) that the person apologizing was legitimately in the wrong, and that they will endeavor to not do that again.
It's that last bit that is important. It's not sufficient for a company to apologize for dumping oil in the ocean or a person apologize for using a racist term. A real apology acknowledges harm caused, and shows how the entity apologizing will rectify past harm and prevent future harm.
This is why, in my opinion, at least, so few apologies legitimately improve anyone's standing. It's not that "cancel culture needs heads", it's just that people expect to say, "I'm sowwy", rub their toes in the dirt, and be let off the hook without doing anything to really undo the harm caused. People rarely even acknowledge the harm they cause, let alone do anything about it, in these so-called apologies.
So no: people who demand apologies don't just reject them after they're given. It's just that most of the time, the apology is meaningless.