There's a lot of discussion of if it matters or not, and some very good shooters seem to fall on either side. The platform and use matter too, if you just care about getting an AR15 to 600m on steel that's less important than taking a 6.5 to 1200m or farther every tiny bit matters. From my reading it seems like most of the military teams, and other precision AR shooters are absolute NOT just slapping a barrel in that has a loose fit, tightening the nut and not worrying about it. The way I see it we spend a TON of time, money, effort etc. putting one of these guns together, better to do it and not need it, than need it and not do it. It's like bedding an action, it might gain you nothing, or it might make a difference, but it's unlikely to hurt anything unless you do it very wrong. At the end of the day, there's a reason why bolt action rifles do not have slip fit interfaces, they are threaded for a reason. The few that do use a press/slip fit are glued into place or they are very tight heat/pressure press fits.
The AR was never ever designed to be a precision platform. If a slip fit was just as good, every switch barrel bolt rifle would be using it because it's faster/easier/cheaper. If you don't think that the military armors/competition teams have not tore about every single aspect of the AR over the last few decades and do a lot of tweaks/mods that really do make a difference, you are just fooling yourself. Joe Carlos spent over a decade on the Army Reserve Marksmanship Program as both a shooter and an armor and one could do a lot worse than to listen to his videos on accuracy issues and the AR and what has worked and what has not. Those teams have spent decades trying different things just to increase accuracy tiny bits, and they have decades and millions of rounds of data to draw on. When they make suggestions on improving AR accuracy, it pays to listen. That said tolerances, and such have improved a lot over the last 2-3 decades and many times barrels already fit pretty snug at least compared to 30 years ago so the impact is even less today if you start with good parts.
The old school, cheap, fast, way was to use shim stock and one of probably 2 dozen different recommended loctite, bearing retaining compound, epoxy, rockset, gasket maker etc. like fluids depending on who you ask. It was the best option then, still works today, but I only like it if you can get a shim combo where you can basically wrap the entire extension. I never liked the idea of having the shim on just one 1/4 of the barrel etc. I wanted it to generally center the extension which meant it had to wrap 3/4 of the way around or so. In fact I'd favor a bit looser fit with a thinner shim to get it all the way around than I would a thicker shim I could only shove get 1/4 of the way around. I'll do this on a factory barrel if it's sloppy just for giggles. Brownells sells a shim stock kit that's not too expensive and contains a few thicknesses.
The more expensive, new, better way IMO is when you have your barrel made you ask them to use an oversized extension, and send them your upper receiver. The extension should be turned down to the point that it is a pretty tight press fit when the upper is heated, some are even still using some sort of loctite with that as well. I ask to have this done on ANY upper that gets a custom barrel now, it's not that expensive and having a better fit never hurts, worst case it doesn't help.
As to the question of bolt carrier tilt, it makes sense it does impact things, as the square bolt face is not square with the round in the chamber if the carrier is tilted. The bolt naturally wants to tilt down at the back you can see it easily with a bolt slid into the upper, and measure it. Match bolts are built up more in the front half of the bolt to allow for less tilt. Beyond that I've seen where some are even tapping and threading holes in the bottom rear of the carrier and putting set screws in them to force the carrier centered when at rest. The same is true of bolt fit in the carrier, some have a lot more slop in them than others. These days with parts like JP, Youngs, Baer etc. they've already done a lot to minimise carrier tilt and bolt slop by being able to reduce tolerance variation.
