*delurks to answer OP because*
The things I allow/disallow depend on any combination of
- What suits my campaign
- What won't get me totally overwhelmed
- What the players want (or don't want).
With the last one, I should note, I have had players actually request to stick to core only as much as possible. I think there's an assumption all players want all the toys but some folks get overwhelmed by options and prefer to keep it simple, especially in as complex a game as Pathfinder is--especially if they're new to the system.
My main campaign world is one I built presuming everything in core existed. It's built around that. Anything added on top of core is stuff that makes sense for the world. Beyond core, I usually only allow inquisitor and cavalier for classes. With the ACG out I might allow Brawler and Slayer. I will often allow up to most of the "featured races" in ARG, although which ones may be campaign dependent (if the game takes place in the part of the world where orcs and goblins are prominent citizens, then they may be allowed; they might not be somewhere else). I remind players of unusual races they are going to have to deal with possible prejudices/unusual reactions, etc.
Why I allow so few classes is for a number of reasons -- but mainly it's because most of the new classes are spellcasters and I want the origins and methods of teaching of magic to be somewhat limited---it's not a low magic world, but the sources of magic are more than finite and it just doesn't manifest in people more than in a few certain specific ways. (Sometimes I consider oracles and witches for savage races or folks from the past, as alternate "schools of thought" for approaching magic.) The world does not have firearms (magic is the technology of war and considered more reliable than steel tubes liable to blow up in your face), so gunslingers and alchemists with bombs are out (I've also always felt like bomb was a weird class feature--how come only they can make and throw them? They're bombs. It's weird.). But more to the point, it also just gets overwhelming to me to have to learn all the different classes and what they do and how to adjudicate their abilities beyond a certain saturation point of stuff. My brain is only so capable unfortunately--and I'd rather spend my time writing more adventures than memorizing new mechanics.
But what I'd allow or disallow in another campaign world might be quite different (I've thought of a more steampunky campaign where alchemists and gunslingers are prominent).
And again players--they want to keep it simple, I keep it simple--if it's too overwhelming for them to play, no one's having fun. They want to add stuff, I review it and see if it suits and make sure others are okay with it.