There's a lot to say about this, really. Personally I'm in favor of respecs, but with a few caveats
Core stats (Splat, Subsplat, subsubsplat) should not be allowed to be changed unless there's a way to change them in-game without penalty normally (and if there is a penalty, that should be charged post-respec). Like, Mages can concievably change Orders, but not Paths.
Stats are more fluid, and depend on the rules of the game. If the game requires justification, then no -they should not be allowed to respec. If the game blanket does not require justification, then all stats should be allowed to be respecced save for cgen only ones. If the game requires partial justification <For, example, supernatural powers> then only non-supernatural stuff should be allowed. As a personal tilt, I hate this last idea - not only because of it being too fiddly, but because it's too sphere-specific and you won't find any degree of balance across something that should be balanced.
As far as what stats should be allowed if a respec is permitted? I'm in general favor of not limiting them - especially if a game offers 'catchup' xp, or has changed the amount of starting xp over the course of its lifetime. In such a case, newer characters would have more to spend, and could allocate things in a more efficient way (especially if we're talking 1e) than someone who started with less.
But really, the answer to most Respec problems is to just go 2e. Flat costs for everything removes much of the urge to min-max stats at chargen, and makes respecs a legitimate use for changing the direction of the character proper rather than trying to maximise spends.