Yes, beer would be acceptable in moderation by the Puritans and their Protestant descendants. Early Americans advocated temperance rather than complete abstinence. Much of this was a result of seeking a better/perfect society after the American Revolution. Evangelical Protestants spread religion and reform through the USA in what is known as the "Second Great Awakening" from 1790 to 1840. During this time, the temperance movement gained support. This led to a gain in popularity of complete abstinence from alcohol and the formation of various groups advocating for teetotalism. Through the late 1800's and early 1900's prohibitionist movements gained traction including the Anti-Saloon League which was driven by evangelical Protestantism. It was this organization that ultimately led to the Eighteenth Amendment of the United States constitution being ratified and prohibiting sale and manufacture of alcohol.

It has been a battle ever since. The area I live in only recently allowed the sale of liquor in restaurants and bars and still does not sell liquor by the bottle. There were many movements that had influence so perhaps it isn't fair to lay the blame solely on the Puritans, but they did have great influence in regards to alcohol in the USA and the parent isn't wrong, but has certainly omitted details.