Marijuana and cocaine were banned at about the same time as alcohol. One interpretation was that this was a side effect of the temperance movement. (This is more clear in the case of cocaine, which was a dry run of prohibition; less clear with marijuana, which was banned later.)

I think the ban of Marijuana in 1937 was a win for DuPond business interests. From a right/left perspective of the 19th century that's difficult to parse as either left or right.