You have a nasty habit of trusting the wrong people. You will lose people who you thought were your friends. Most of them won't apologize and probably won't ever think that they should. Here's to the ones that do:
It's not okay.
You shouldn't care what you did to them, because, frankly, it doesn't matter. You deserve to be treated with respect. You deserve to be treated like an adult. You don't owe anyone anything.
Even if they are trying to reconcile, you don't have to accept.
Even if they really are sorry, you don't have to accept.
Even if they feel guilty, you do not have to accept.
It's not okay.
Not accepting an apology and not moving on are two totally different things.
Another article on this site discusses how you are only hurting yourself if you don't accept (even nonexistent apologies). The author equates not accepting an apology with failing to move on and overlooks the importance of coming to terms with what happened.
Her claim is sound: you are only hurting yourself by hanging onto that anger, but her argument is too hung up on "not [giving] the person the satisfaction of knowing that they have so much control over you." Moving on means not caring how the other person feels about your process. Whether they are satisfied by it or angered or saddened or whatever is irrelevant because how they feel has no effect on you.
That's not to say that moving on is easy. You need to go through your own process in your own time and that's okay too. The author of the other article talks down to you in telling you to "put on your big kid pants and move on," but this trivializes emotions, and betrayals are not that simple.
When a friendship falls apart, you might feel guilty and angry and sad. You might feel bitter or vindictive. You might want to scream at them or curl up in your bed and sob. Telling someone to just get over it is not only dismissive of the nuance of emotion, but also of the hardship of betrayal. If it takes you two days to move on, that's great, but two years is also okay.
She's right about one thing. They probably will never apologize and they're probably never gonna feel bad. However, you don't have to forgive what they've done in order to move on.
It's not one person's fault.
Nine times out of ten, if two people can't reconcile an argument, they probably both did something wrong. Of course, there are times when one person is just being awful, but it's usually not so black and white.
People make mistakes. You make mistakes. That's okay.
There's probably problems on both ends of the argument. You're probably a little bit guilty. They're probably a little bit guilty. You can still move on.
If you don't want to accept, you shouldn't.
Just like if you can move on quickly, if you are able to accept their apology, that's wonderful.
However, choosing not to accept can stem from many reasons. Maybe you can't trust them. Maybe what they did was too severe for a sincere apology to reconcile. Maybe you just don't want to. You need to do what is healthy for you. And whatever is healthy for you is okay.
You deserve to keep good people in your life. You deserve to cut negative people out. You deserve respect.
You don't owe them an acceptance just because they did the right thing in apologizing.
The most important thing is that you take care of yourself.
So, do what's best for you. Do what you can to be healthy. Sometimes, it's gonna suck, but you'll be okay. Take it from me, you don't have to accept their apologies.