Street drugs do not stop you from going Clear and OT. I know of several people who started out getting treatment at Narconon and eventually made OT levels (some all the way to OT VIII). (One reverted to heroin abuse well after Clear)
LSD and PCP stop you from being eligible for the Sea Org. You can still be staff at a local (non-SO) org. You can still pay for your Bridge, no problem. There are several "drug handlings" done along the way: Purification Rundown, Scientology Drug RD, New Era Dianetics Drug RD, OT IV which is a drug RD for your BTs.
(Then of course, if you get in trouble with OSA and get SP declared, it doesn't matter if you have stayed perfectly clean for fifteen years and have gone through every drug handling the CoS has to offer, plus all the OT levels, your declare will still say you're a druggie - happened to someone I know. The CoS obviously doesn't quite believe in the power of the tech.
People who have taken "psych drugs" (incl. antidepressants, sleeping pills, sedatives) or have been getting care at a psychiatric clinic (even if just for one night) are not supposed to be accepted for auditing, and would not be able to go Clear and OT at an org. However, there used to be a possibility to write a petition to the org, where such a person gave up all rights to refunds or to suing the org (some former psych patients do have a bit of money they need to be "cleared" of...) As I recall, they could still have problems to be accepted for OT levels, depending on how heavy the "psych treatment" had been.
It's quite possible they are stricter nowadays on not accepting takers of psych drugs for auditing. They can still do courses, though, and be told to find somebody to co-audit with in private (not in the org). They would not qualify for Sea Org.
As Freeborn said - the key is that the person has to know and honestly tell about having taken the drug.
And I don't know exactly where the line would be drawn - isn't it usual for people to get sedatives before major surgery, for example? There are medical drugs which are used for both psychiatric and non-psychiatric conditions - an anti-epileptic such as Tegretol is used to control seizures (a neurological condition) but also as a mood stabilizer in for example bi-polar disorder. This is where Tory Bezazian had trouble - the org suddenly decided that her anti-seizure treatment was an evil psych drug. Later, this decision was reversed. The point is of course that in modern medicine, there is increasing knowledge of the physical body dysfunctions that are associated with psychiatric conditions, and there is no sharp distinction between body and mind. It's all extremely hard to align with the CoS world view.