Some factions are summed up by their leader.
Durwin Darkweather rose to prominence as the most tenacious lawyer in the city of Blackcrag. As disagreements arose over inheritance and ownership of the increasingly crowded and prosperous city, Durwin found ever more work coming his way, and he took it all on.
This so impressed Lady Erven that she recommended Darkweather for position of judge when the previous judge died of extreme old age. The monarch agreed, and for the past fifteen years Darkweather has spent about 9 months out of the year traveling to nearby cities and towns to hear their cases, and spends the rest of his time in Darkweather Manor, a drafty old house in the middle of Blackcrag's High District. He and his young wife, Dulcina, live there with half a dozen servants, most of whom travel with them.
Over the past decade, he's handed out increasingly harsh punishments for crimes that involve drunkenness. He sees alcohol as a pernicious vice, at least partly responsible for a high percentage of crimes but completely unregulated.
This spilled over into a public concern five years ago with several nasty crimes committed over a single three-week period. (Their severity is up to you and how harsh you want to go with your players, from public revelry gone overboard to alcohol-induced beatings of disadvantaged residents to drunken child abuse.) Citizens began taking to the streets in protests, initially against the acts themselves, then shifting into demonstrations against hard alcohol. Judge Darkweather attended and gave spirited speeches about the evils of liquor.
(If you're playing in a more accurate Medieval setting, nobody would dream of outlawing ale. Clean drinking water is too precious; everyone drinks ale. In this case, the abolitionists are calling for a ban on hard liquor only, but this makes the owners of the city's alehouses and taverns doubly nervous. If hard liquor is eliminated, how long until ale?)
As a friendly faction, the abolitionists are simply a group of concerned citizens who want to stop a vice that's grown over-abused. Play up the role of hard liquor in gambling dens and other houses of ill repute; perhaps most of the alcohol in the city is consumed in such places, and it's used primarily to lower a sucker's inhibitions.
Judge Darkweather uses his connections with the City Watch to learn about large shipments of alcohol, and he'll hire adventurers to follow those shipments to whatever illicit establishment they inevitably end up at.
As a foe faction, the abolitionists have grown from a few concerned citizens into a mob secretly controlled by organized crime. Certain shady individuals have made deals with Darkweather to push this agenda and turn a blind eye to their bootlegging operations if the abolitionists get their way, in return for hefty bribes now and in the future.
Why did Darkweather agree to this? Perhaps he's greedy, or perhaps his back is up against a wall from another direction. Perhaps it has to do with his strangely childless young wife....
The criminals involved in this arrangement use this opportunity to ratchet up the situation, including liquoring up stooges and framing them for horrible crimes.
- (Friendly) Judge Darkweather summons the PCs to Darkweather Manor, where he explains his stance on alcohol and offers a fee if the PCs will follow a shipment of expensive brandy that's coming off the docks that night. The PCs are to find out not just the building to which it's delivered (that might just be its first stop), but where it's actually being drunk.
- (Foe) A teenage girl nervously approaches the PCs and asks them to speak with her brother, Abel, who's being held in the castle for trial. Last night, Abel was found passed-out drunk on a back street, clutching a ceremonial sword that belonged to a noble's son who'd been viciously beaten to death earlier that night not far away. Abel and his sister swear he was framed. An investigation will lead to an organized crime lord who's, oddly, setting up a secret massive distillery....
Art found online without attribution, sadly; even a reverse image search reveals only Pinterest boards.