Instead of a binary, you can also ask what policies would they have supported. Perhaps they would have supported a policy that preserved individual choice while creating substantial friction between users and drinking as well as limited the profit incentive get people to drink more.

It's worth noting that the most lethal drugs are the legal ones (measured by total fatalities). Take tobacco for example. It's been around for millennia, however we did not get the modern tobacco epidemic—which killed 100 million in the 21st century—until A) mass manufacturing of cigarettes, B) heavy engineering of cigarettes to be hyper palatable and addictive, and C) modern mass marketing. This is why I'm partial to the tobacco endgame proposals that focus on removing the profit incentive to get people to consume addictive and/or harmful substances. Consumption in society can be managed to a point of acceptable trade-offs by friction and nudges once you remove the asymmetry of multinational conglomerates spending billions of dollars to get adults (and yes, youth too—the majority of smokers start when they are minors) to consume tobacco and alcohol whilst effectively lobbying for much weaker regulations than recommended by the public health community.

This kinda reminds me of a post that asked if EAs would have been as in favour as the abolition of slavery as a particular extremely hard-line anti-slavery activist at the time who we morally laud today as a moral exemplar, but who everyone at the time thought was a shocking PETA-type extremist. (Found the post)

The comment posed by @emre kaplan🔸 there I think is very illuminating.

Scott Alexander somewhere on the forum wrote a comment I mostly agree with (where he was giving caution to a pro - Pause AI post, cant find) that most, or at least a significant amount that we cannot discount, amount of social change comes as a consequence of people that want change working from within the system and gaining high status from within the system to be able to affect change - because the people who have the power to then make change like these high status people and want their respect.

This all just leads me to the fairly obvious conclusion that like with AI Safety and Slavery Abolition, EAs - hypothetically placed at any place in history - are most likely to be found working within a system gaining enough status to slowly and reliably tweak the status quo in a positive direction. 

There is no contradiction between being opposed to Prohibition but in favour of finding a reliable way to get people to drink less alcohol.

In some ways, Prohibition didn't seem that bad to me?

There are two clear arguments you bring up:
1. If the government could effectively ban alcohol, it shouldn't, because doing so is anti-liberty.
2. The government won't be able to effectively ban alcohol.

It seems like (2) is a policy question. I think that today, most liberals are often on the side of drug legalization, especially because they question (2). 

Personally, I don't have massive problems with (1). There's a concrete question on if alcohol is net-harmful, and if so, is this something the government should prioritize. There's a lot of empirical questions to ask here. That said, if it were the case that alcohol were net-harmful enough, and I thought the government could net-effectively ban it, that seems good to me. This is the kind of common question where utilitarians and libertarians would often clash.

All that said, as pointed out in other comments, a "total ban" is often the ideal policy (taxes seem better), but sometimes other options are just too complex / unpopular. 

Lastly, note that Prohibition ended, and now we have more information. It lasted from 1920 to 1933, a fairly short time for a major policy. I'm a big fan of trying out certain policies, then canceling them if they are clear failures. (That said, I could certainly imagine cheaper experiments than a national-level 13-year ban)

I think the answer depends on if we are assuming if prohibition-era EAs have access to the same analytical tools that we currently do. Specifically I think the reason to advocate against prohibition today is that prohibition 1) ignores costs of a black market / enforcement 2) ignores the welfare / pleasure gained from drinking.  This would then mean prohibition is  an analytical error more so than a change in ethics

It's still true that alcohol (also gambling, added sugar, and tobacco) creates large social extranelties while addiction stresses the definition of having rational preferences. Yet the go to tool for these behaviors is sin taxes. I think setting a sin tax high enough to reduce harm (ideally setting the rate so the loss in the "benefits" of drinking equal the social costs) would remain the go-to solution if past EAs had access to to modern welfare economics and tax theory. Without the historical lesson of prohibition gone astray or the success of sin taxes in general, I find it hard to imagine that "half" measures like taxes or public health campaigns would win out against the maximalist arguments against preventing alcoholism especially when we are all affected by the cultural norms of the day.