Samples of .223 casings out of my Mini 14. All have been polished.
The one on the left is after I re-sized it (Full length RCBS)
What is causing this?
Will it go away as gun breaks in?
Do I chuck these or reload and use?

So you're saying the ones on the right were shot and not touched after they were ejected and the one on the left went through your RCBS full length resizing process and still came out looking like that? Normally the first thing to look at when you resize and have a dented casing is that you're using too much lube or you haven't got your die set up in the press properly. I'll defer to the expert reloaders on here because I don't reload that much stuff to offer anything else. Was any of that ammunition from the factory or all of it reloads or what? It appears the rifle needs to be thoroughly examined by a competent gunsmith who can check the chamber, etc. Are those .223 or 5.56rounds by chance, as if they are the latter that could be your problem from what I've read on those very similar rounds but that they shouldn't be interchanged due to pressure variations?

Factory .223. UMC's. The gun is 14 tears old, very little rounds through it though.
Didn't over-lube. ALL have been through the polisher.
The one on the left that has been re-sized fit easily in the chamber where the others did not. I think it's common on these types of rifles to get dents like this. My son's AR does the same thing.

I'm not into the ARs, so I can't make a comment on it being normal, but I don't know why it would be. If it's denting them when it ejects them is one thing and if it's caused by a chamber issue is another.
EDIT: I googled this problem and there is actually a lot of information on the net. It is basically caused when the casing is ejected and hits a part of the receiver and they are usually in the same place on each particular gun. Bad dents may cause a problem if you want to reload them, but shallows dents will probably be fireformed out during firing and then it will have another dent upon ejection. If you can determine where they are hitting, some guys are using several pieces of electrical tape, believe it or not, to soften the contact and they claim that takes care of the denting problem.

That is normal for that type of rifle. Load them up and shoot them..

I'm going to add a "softener" in a likely spot and sned some more downrange.

Don't sweat it...common problem with Mini's...both mine do it as well...load em up and send em down range...

Very common problem with Mini's. I used to shot them for the State Match Pistol and Rifle Team and all our brass used to look like that. We used to shoot Fed. Gold Match and Rem. Match. Still have several 5 gal buckets and it all looks like that. I just load it and go. Coyotes and Prairie Dogs don't notice it. Or at least they haven't said so!!! LMAO!!!!