So far:
1. You must anneal every firing
2. You should anneal regularly
3. Only use AMP annealer or don't bother
4. Never anneal. Ever.
This is like religion.
Here are some things to always remember:
1. Different shooting disciplines have different requirements. A load that will shoot a perfect score in F-Class may be mediocre for a benchrest rifle. An LR BR shooter can get by with mediocre wind reading skills, but and F-Class shooter cannot. A Silhouette shooter doesn't need a BR or even F-Class level load, but does need to be able to shoot offhand VERY well. A hunter needs a moderately accurate load in a reasonably portable rifle.
2. Most approaches that are arrived at systematically and consistently will work. There are many ways to bake a cake. The only sure way to know anything is to test it for yourself........and then test and continually refine your approach.
3. What method works best is a moving target. Decades ago, neck-only sizing helped accuracy. Then we noticed that after 3 or so firings that the bolt was hard to close and we had to FL size occasionally anyway. Then we all figured out that we actually got more accuracy by FL sizing and bumping the shoulder .002ish and everything was more consistent.
Annealing used be be a dark art, and that may be why Neil Jones said to not do it--he has been around for a VERY long time. Shooters would shoot brass until it started to have issues with spring back then they would anneal. Using a torch and case in a drill, results could vary.
Then better and better annealers started showing up, making annealing fast and correct. We also got more accurate rifles, better bullets, more accurate loading processes, and we got better at tuning rifles. With this higher level of accuracy we noticed that the load needed to change after annealing when we only annealed after every few firings. We only learned that because we shoot much smaller groups than we used to.
That is why guys shooting high accuracy disciplines either anneal after each firing or don't anneal at all. Brass slowly and consistently changes after each firing when it isn't annealed. It will last until it work hardens and quits shooting well, assuming the primer pockets hold, the head doesn't start to separate, and the necks don't split.
Annealing all the time keeps the brass in the same state of hardness for each firing for as long as it lasts. However, if we shoot brass several times then anneal, we introduce a big change in the hardness. This shows up in high accuracy rifles and may require a load adjustment.
4. Not everyone constantly refines their processes. This is a big reason why you see such variance in methods. When I first started hunting and reloading in the 70s, a hunting rifle that would shoot 1 MOA was considered super accurate, and a long range BR rifle that shot a 6.125" group set a world record. Nowadays, a 1 MOA hunting rifle is considered mediocre, as is a 6" group at 1000 yds.
However, if a guy had found a 1 MOA load for his hunting rifle 30 years ago, and had taken dozens of animals at distances to 500 yds; you'd have a hard time convincing him he wasn't doing things well. He probably FL sizes his brass, doesn't anneal, and uses an old RCBS press with standard dies. He may even tell you all this new equipment and methods are a waste......and for him they would be. He obviously went out and DID IT and knows what works for him.
We all have to earn our place by testing this stuff for ourselves, and not be concerned that guys have differing opinions. We have to pick a method and go try it. It really doesn't matter so much WHAT method we choose as it is HOW we do it. Once we start testing a new method, a lot of things become clear.
5. Understand who you are getting input from. If you want to shoot small groups at long range, listen to LR BR shooters. If you want to learn how to read wind, talk to an F-Class shooter. If you want to be better at shooting offhand standing, talk to a Silhouette shooter.
Also, Instead of trying to get people to persuade you, work to understand the overarching principles behind what people are saying. Then go try it......