I think people have already hit on most of the prejudices that would come to mind for me but all I'd say is that a whole lot of the prejudices drug users get are either the same or very similar to those with any kind of mental illness, depression, anxiety, etc.
Some of them are different because at least SOME people realize that having mental illness is something that is generally at least SOMEWHAT more out of your control than your drug use and it's hard to view being mentally ill as "hedonistic" in the same sense as drug taking, but by and large those who don't use drugs or having mental illness view both types of people as being weird, possibly dangerous, sick, incapable of being productive members of society, lazy, entitled freaks who blame their issues on society or aren't willing or able to "man up" and deal.
The mental and emotional experiences of both drug users and the mentally ill are generally not considered relevant in the same way as those that "normal" people have to deal with, they are seen as "1st world problems", that would simply "go away" if they were forced to deal with more "real" issues like fighting for survival (as if that's not something both types have to do regularly in different ways), and the feelings and thoughts both types have are considered very "questionable" in their worth, or really whether or not they are even "real" at all by "normal people".
Normal people think both types are always asking for "hand outs" (not that there aren't some who are SOMETIMES), who are incapable of helping themselves, and who are not worth wasting time on or around, and also, on lots of dating sites I see women post on their profiles that they are unwilling to date guys who use drugs or have any kind of "mental issues" and every time I see that (and I've seen it A LOT) I get pissed off at how judgmental those girls seem.
So yeah, there's a lot of similarities, and of course lots of drug users have mental issues and vice versa.
On top of that is of course the paradox that while there are unintelligent, lazy and mean drug users and people with those same qualities who are mentally ill, both categories of people also often have members who are highly intelligent, artistic, empathetic, and capable of offering society certain things that are quite unique which under certain conditions may be impossible for "straight" people to offer in the same way.
As someone mentioned before, many of the shamans/medicine men in certain native cultures were drug users, and also many of them had mental illness and also many of the great geniuses and artists of society were drug users and/or had some mental issues.
I read recently on some facebook link that Native shamans of various cultures believe people with mental illness like schizophrenics are actually mystics who are gifted and who would make good shamans and that when they have seen how these people are treated in mental hospitals they think it is absolutely horrible.
It generally comes down to fear from "straight people" with both drug users and the mentally ill: they cannot understand or interpret the way these people think and realize they may be more difficult to program societally speaking and so they shun them.