I hate it when people say stuff along the lines "it's not required, and thus ok, because you have <insert completely unreasonable alternative here>".
Well, the reasonable alternative in this case is to just not get involved in school sponsored extracurriculars. Should have been clear on that point.
As said in the first post, parents can also sign a paper voluntarily to for you to be forced to take random drug tests and the school can then inflict whatever punishment they see fit. It's not just when joining clubs, although it is required to join the clubs, as well.
The larger issue, as noted here, seems to be parental oversight, for which removal really is the only choice, either by emancipation or adoption. You can't really legally force parents to treat their children in ways beyond certain basics (no abuse, etc), in the current system. There's not really anything in place to ensure that parents are good at what they do beyond those basics, for which stuff like privacy (beyond the point of preventing sexual abuse) doesn't enter into the equation. A parent requiring a child to take a drug test and consenting for the school to handle the repercussions involved is well within their rights as a guardian of a dependent.
It's even fairly reasonable from a moral standpoint. If someone is providing necessities for you, such as room and board, and you don't have some sort of arrangement for those services (job contract, equitable labor, etc), then it's fitting they can put certain restrictions on your actions.
If you're saying that those underage should have better recourse for finding employment and making it so they're self-sufficient, and thus able to separate themselves from the guardian/dependant relationship, that's something that sounds fair. The drug testing scenario given isn't outside the rights of a parent, though.