Belling the case mouth for a .243 is a new one on me. The case mouth after full length resizing, trimming to proper length, should be de-burred on the outside, and especially the "inside". Sounds like you have missed this step. Chamfering the inside removes any burrs that might still be there, and acts as a guide for the projectile you're trying to seat. Boat tail bullets take very little chamfering to guide the bullet in, but if yours is a flat base, a little more might be need to get the job done right. Some of the reloading manuals have very good instructions with pictures to help you along with this little bit of information. Also, are you using the correct configuration in your seating stem?
Not unusual.
Virgin brass and non-bushing sizing dies run a little more neck tension than necessary and you'll get some shaving once in a while.
Pistol cases get a belled neck. Bottleneck rifle cases like the 243 should not get a belled neck.
I know you said you chamfered the necks. You just aren't chamferring enough if a ring of copper is being peeled off. Prove me right or wrong by taking one case and chamferring the neck until it is so sharp, it could be used as a leather punch. You can't overdue the chamfer, it just takes a lot of extra time to over-chamfer.
Pistol cases get a belled neck. Bottleneck rifle cases like the 243 should not get a belled neck.
I know you said you chamfered the necks. You just aren't chamferring enough if a ring of copper is being peeled off. Prove me right or wrong by taking one case and chamferring the neck until it is so sharp, it could be used as a leather punch. You can't overdue the chamfer, it just takes a lot of extra time to over-chamfer.
To your question, no it won't effect pressure or accuracy in a run of the mill factory rifle used at normal hunting distances.
I too, don't understand the comment about the configuration of the seating stem.
You just need a couple more twists with the chamfer tool.