But it was surely something MANY on right also pushed in.
It's weird, but at times, some peoples on opposed lines may agree. Social-conservative right, I can see pushing for this as well. Libertarians and such, not.
THe Prohibition is as much rightwing as left.
I'm not sure. As others have said the modern political views don't really fit 100 or so years ago, especially considering how much Progressives were supporting Prohibition IOTL, They are considered the ancestors of the modern left by the modern left while having a level of religious fervor equal to or even exceeding the modern religious right.