This is partly my opinion, in that I believe the attempt at Prohibition was a complete failure. Having said that,
A functionalist considers how each part of society contributes to the stability of society. The anti alcohol folks felt that they could make society better and more stable by getting rid of alcohol. They looked at workers wasting their pay on beer, families left without food, men (generally) drunk in the streets, and believed alcohol should not be allowed. They did not consider the other side of the alcohol question, including drinking in moderation and the unfortunate fact that people who work menial jobs for little pay like to forget their troubles for a time with drink. Prohibition simply sent alcohol underground with huge illegal operations and bootleg liquor. A functionalist might say that Prohibition traded one type of instability for another and therefore was a failure.
A conflict theorist views society from the communist perspective, in that society has factions which compete for money and power. The religious factions who did not drink wanted to use the power of the law to prevent others from drinking. Partly this would be a class and cultural struggle between those whose cultures included alcohol (most immigrants, Germans, French, Italians, Irish) who were often the lower classes, against the well to do white Protestants who did not drink alcohol. However since the police, who were supposed to enforce the law, were generally from the lower classes, they mainly turned a blind eye or got their cut of the money generated from bootleg liquor. The destruction of liquor production hurt the German brewers and wine makers of the Midwest, while people who could get liquor illegally and sell it made fortunes (it is said that the Kennedy fortune came from this), and of course the Mafia was involved. Thus the era was full of conflict,and those who wanted to eliminate alcohol failed.
An interactionist views society as made up of individuals who have many and varied interactions between each other, creating life and a sense of self and creating meaning. The people who pursued Prohibition would be viewed as well meaning people (mainly) who saw alcohol as evil and dangerous and who wanted to help force drinkers to mend their ways. Obviously in order for the amendment to be passed a lot of people believed it was a good idea. For them, alcohol was not a way of life (as opposed to a German beer maker, for example, or a coal miner who wanted a drink at the end of a hard week). They likely saw the damage from drunken behavior and wanted to stop it. However there were many more people who liked alcohol, for enjoyment, to forget their troubles, and as a business. There were people who overused alcohol and those who did not. For them, wine or beer at a family meal was part of their culture. Drinking to excess was not entirely disapproved of. (Consider the college campus now or the society of young professionals.)
I would suggest you see if you can find some specific references on each theory and see if there is anything in the sociology literature about each of the 3 theories and Prohibition.