They are, but they are also actually less new of a phenomenon than we typically believe, just because we have a more direct view of the present than all of the expanse of the past. There used to be many such "moral entrepreneurs", pearl clutchers, moral busy bodies. We just had different words for them, but some of the SJWs of the past have been no less self-righteous and unhinged. As an anecdotal example, here is the axe wielding Carrie Nation:

https://en.wikipedia.org/wiki/Carrie_Nation

Carrie Amelia Nation (forename sometimes spelled Carry;[1] November 25, 1846 – June 9, 1911) was an American activist who was a radical member of the temperance movement, which opposed alcohol before the advent of Prohibition. She is noted for attacking alcohol-serving establishments (most often taverns) with a hatchet.

Nation was also concerned about tight clothing for women; she refused to wear a corset and urged women not to wear them because of their harmful effects on vital organs.[2] She described herself as "a bulldog running along at the feet of Jesus, barking at what He doesn't like",[3] and claimed a divine ordination to promote temperance by destroying bars.[4]

One could wonder if the whole project of Temperance and Prohibition was something akin to a huge SJW movement, not unlike the more recent Satanic Panic or the furor about video games.

This is not to say that we shouldn't be pushing back. I am not saying:

"Oh, this has always been a phenomenon. Just wait and it will go away."

No, it means that this cultur war, or whatever you want to call it, has always existed in one form or another. When people ask "When will this finally be over with?" the unfortunate answer is "Well, never." The social struggle towards equilibria between control and liberty will always be a constant and every generation needs to fight it anew. It does not mean we can give up, because the other side will never give up, either. It is not unlike a struggle between good and evil, but one should be careful not to write off the other sides as simply evil. The culture war will never be won but will always have to be fought. Forever.