In any eyepiece barrel equipped with a safety undercut there are three zones:
1. The uniform section above the safety undercut.
2. The uniform (rectangular) or non-uniform (tapered) safety undercut.
3. The uniform section below the safety undercut.
As long the uniform sections 1. and 3. engage with the uniform bore of the focuser or adapter, how can the safety undercut influence the registration of the eyepiece?
There is one situation that I have encountered in which a tapered safety undercut plays havoc with the registration or collimation as per the OP. And that is when you're using a Howie Glatter Parallizer with wider bodied 1.25" eyepieces.
Since the wide body engages the sides of the conical throat before the eyepiece bottoms out on the seating shelf, the upper uniform section, as per 1. above, may not engage fully over its entire depth. This is due to the unique, non-circular cross section of the bore of the Parallizer.
As a result the eyepiece can actually tip over when acted upon by the single set-screw on the opposite side. It does this because the narrower upper part of the tapered safety undercut can actually pass into the 'bulge' cut-out in the bore of the Parallizer.
I solved this by removing the flange and the conical throat of the Parallizer thus ensuring that, irrespective of how wide the eyepiece body is, the eyepiece will always bottom out completely on the seating shelf. As such, the upper uniform section of the barrel in 1. will always engage with the bore as much as is intended. With the upper section and the lower section fully engaged, the Parallizer is then able to do its job admirably.
I have no experience using a wider bodied eyepiece fitted with a barrel having a rectangular undercut in the Parallizer and so can not say if the same situation would arise.
Reason for Edit: Spelling, Grammar and an Omission
Edited by Richard Roseweir, 10 July 2015 - 11:32 AM.