No, it is no one's business. Criminalization of drugs is the Christian conservative equivalent of Muslim prohibitions of drugs and alcohol. Christians who bash Islam (justifiably) are hypocritical.
BTW, Christian sharia law has often been enforced, even in the U.S. E.g., "blue laws" and "prohibition".
Now, as to the supposed "social evils" of drug use. If someone is idiot enough to abuse, that is his problem. If someone is dependent on a drug user, that is their problem.
But the religious bit about "brothers keeper" seems to be the justification for everyone butting in to everyone else's business.