The temperance movement was a major force in the late 19th century/early 20th century in some countries, culminating in Prohibition in the US. Though famous for restricting and banning alcohol, some temperance activists also campaigned against tobacco. After the 18th Amendment was passed, one activist proclaimed that "tobacco was next". And indeed, in many states they managed to pass various bans on the sales of tobacco products, which unfortunately were short lived as this part of the temperance movement died out during the 1920s (speaking of the US).
So what if alcohol was always lumped in with tobacco? The Victorian era had an anti-tobacco movement, mainly based in Victorian morality but also inadvertantly in science.
Speaking of the US, I think it would be an issue in states like North Carolina and Tennessee where the tobacco industry was huge. For instance, even though Tennessee had a huge alcohol industry (Jack Daniels is the most famous of the remnants of it), it was all banned even before Prohibition by the state legislature. If the 18th Amendment had included tobacco products, would the amendment have been passed at all, with the struggle it might've faced in some states? Would, as I have suspected, the Temperance movement been hindered by the association with the early anti-tobacco movement? I think it would keep the Prohibition Party as a major force slightly longer, but...