@Monogram here is my outlook on it. Do it. If you're sorry, apologetic, or otherwise feel as though you somehow slighted someone and truly feel remorse for it? Show the other party that you recognize your mistake and are attempting to correct it, whether that means moving on from it and trying to return to a sense of normalcy or leaving them alone.
Why do people hold grudges? The answer is likely as varied as the person holding it over the span of months or even years in our hobby and I'm well aware that I can hold grudges for decades. Why do people hold grudges repeatedly? Well, as we've saw with a member or seven of our community and as you indicated in your post "Oh, I can't believe that X and Y are friends again"; sometimes people act like asses. Repeatedly. We see X and Y being friends again after Y told X they hated them, then six months later they're enemies again when it gets out that X said they didn't believe Y over their self-diagnosed Asperger's. People attempt to forgive, forget, move on, and never stop to think maybe their personalities just don't coincide. Which spawns years of back-and-forth loathing-make up-loathing-make up relationships that we see sometimes.
Sometimes? It's miscommunication and the ability of some people to refuse to be adults in the situation, even only some of the time. Other times one or both parties just want to avoid the drama until it blows over, but it never does. Sometimes it's not even clear what the other party was pissed about, people are finicky creatures at the best of times.
Two or three years ago I was acting like a complete and utter dick to @Coin. He may very well have not noticed it, I only say this because he never mentioned it to me directly and I never brought it to his doorstep. I allowed it just quietly fester. At that time he was running his own game, with multiple people inviting me to come check it out. I refused because he was a (head, I think)staffer and I figured that he'd use his position to be an ass toward me. Fast forward a couple of months and I finally gave in to the repeated attempts to get me onto the game.
You know what Coin did? That jerkoff (I say this with love)? He was nothing but friendly, professional, and overall Chillzilla with me. Maybe he didn't know about our quiet beef? Maybe he didn't care? Regardless, if he did have some inkling of it he gave zero indication and took the high road. This, in turn, made me realize that I was being a childish dickhole. It was on me, not him. This made me reassess how I was treating others and as a result made me want to change how I behaved toward others; selfish, right? Well, change has to begin with yourself. Now? I pop onto Skype randomly to share pictures with Coin, check in on him randomly, make small talk briefly while I'm on there(which isn't often), and generally attempt to restore/maintain the sense of camaraderie that he and I shared a long time ago. Know what else? I've never actually apologized in written word, I've only tried to show that I was sorry for my actions by returning to a sense of normalcy.
But, if I'm wrong about showing rather than saying. Then you have my apology @Coin for acting like a fucking idiot by taking something that could have been resolved early with a simple conversation and blowing it out of proportion. I hope that my actions have shown this to be true.
Now that goes against my earlier comments in this thread about making an apology personal, rather than shouting it in the street. Which makes me a hypocrite now, I guess. It seemed appropriate, oh well.