Actually, drugs were prohibited first, then alcohol.

It just goes to show that if you think that the laws that hit the minorities that you don't like (or even a majority that you don't like) and so its an ok law even if its contrary to your state principles, you leave yourself open to having things you care about hit on the same basis as you let the laws targetting minorities get hit.

The British turned the Chinese into opium addicts, fighting a war with China and in the process ending up with that 99 year lease on Hong Kong, so that British corporations had a base to sell opium into China.

Then when Chinamen in the US who were opium addict were the target of persecution and exclusion, the people that seemed to be the only opium users were the Chinamen so making use of opium a crime was perfect. (And the prosecution of the white people who used opiates was very selection, hitting only those that the politicians saw as enemies.

The same thing happened with pot.

And after the white man had figured out how to process coca for industrial purposes (drugs, patent medicine, and Coca Cola) then what had been a widely used mild stimulant became a high potency stimulant that poor minority artists used, that became a perfect vehicle for persecuting them.

After those steps were taken, prohibiting alcohol was the easy next step. It was like the camel coming completely into the tent after its nose was allowed in with opium, pot, coca, and ripping up the tent.