Basically I think there are two considerations here:

1) The character idea should still be visually identical enough to the playable race that there's no reason for confusion. Your jaette example I think compromises this, as jaettes are described as 'troll-like' creatures with tusks and mottled green, warty skin. No one would ever see a jaette and mistake it for a fire giant, not even at a glance. However a jade elf could easily be mistaken for a wood-elf let's say, and only at closer examination does the viewer in the description see the jade coloration.

2) The idea should not involve any concept in which the character would conceivably have strengths, vulnerabilities, or attributes that are inconsistent from the playable race. Jade elves are the same size, have the same vulnerability to iron, and do not possess any fantastic powers unique from regular elves. Whereas to examine your other example, dryads, should conceivably have various mystical powers, be linked to a tree, and do not share the same vulnerabilities that wood elves do.

Now it's highly unlikely we'd actually stop someone from roleplaying an alternative idea (unless it was something so particularly goofy that it was actively disruptive), it's just not going to be looked upon highly if there are big glaring inconsistencies, and I think you'll find most players react the same way.

So in summary, stick to the standard races or, if you are looking for a bit more exotic of an idea, pick an alternative culture fragmented off from a playable race. This is something commonly done well with humans, such as various barbarians or humans with the Arabic flair of Hamzah Mu'tass, but can easily translate to other races as well.