Were anti-immigrant and anti-catholic sentiments essential to the temperance movement's successes?

Its hard to say if it was essential, but it certainly played a role. During the late 19th century and turn of the century there was a large influx of immigrants in to the cities of America while most people already here lived in rural areas ir s all towns. Saloons and alcoholism and thus abusive fathers/husbands had been a problem for a lot of the century already and so the protestants were already pushing against alcohol. However women and children weren't the ones in power so it was tough to gain enough support to make law changes happen. As the early 20th century went on the disdain for city folk (almost synonymous with foreigners/catholics at the time) grew for a variety of reasons and those people certainly drank a lot. This gave the men previously on the fence or against prohibition more reason to push for it and voilla. In short, I don't think you can argue that an anti-immigrant/anti-catholic sentiment was the sole driving force behind prohibition. Especially considering many states had already experimented with their own prohibition laws. However it is fair to say that it largely contributed to the "success" of prohibiton on a national level. Whether you consider that essential is up to you.

History of Alcohol Prohibition http://www.druglibrary.org/schaffer/library/studies/nc/nc2a.htm