Building plugin with changeable custom post type values…advice needed

I would not give them control over the actual name of the post type. What if they rename it to revision or attachment? Big time site wreckage potential there.

I’d say stick with the more “trivial” things; basically, only those things that don’t go into the database: labels, rewrite settings (although that could be potentially hazardous in the hands of an uneducated user), menu icon, menu position, exclude from search, and supports.

I think allowing GUI management of those things would give the user the most flexibility without compromising stability.