The so-called progressive movement, which now fully backs the vaccine mandate, has NEVER been for the War on Drugs, even when it hadn't failed. And the kinds of behaviors that the political left regards as protected vices are not limited to those engaged in by addicts. For example, high-risk sexual activity that leads to HIV infection rates 100X higher among gay men than the general population, is not associated with any addiction, and yet the vaccine mandate supporters by and large would be the type that would be aghast at any suggestion of deterring such behavior with punitive government measures.
As I said, the current mandate and OP are matters of workplace safety. You cannot contract HIV under normal workplace conditions, so it is not equivalent or germane to this discussion. Likewise, employers in the US are free to require invasive tests for drugs and alcohol at will, and discriminate against those who abuse them.
I'm not addressing your characterization of a particular group of people (liberals) because that is 100% your opinion and largely speculative.
This thread, and the OP are discussions of a vaccine mandate for workplace safety. OSHA has wide authority to regulate workplace safety and implement standards.