How does the movie "Gangs of New York" relate to actual history? Is it historically accurate? Elaborate for both sides of the argument.

In broad terms, the 2002 drama film Gangs of New York is accurate. Its accuracy is principally episodic. That is, the large-scale events depicted in the film are true. There were, for instance, draft riots in New York during the Civil War. And, New York during this period suffered both communal tension and gang violence, with a large number of Irish immigrants concentrated in the notorious "Five Points" neighborhood. In reaction to that influx of immigration, there was during this period a strong nativist reaction, another accurately portrayed element of the film.
What is either left out of the film or modified in a way that is not historically accurate are some of the personal representations. The film sees a large presence of Chinese immigrants. In fact, by 1870 there were only about 200 Chinese immigrants living in New York City. Historians have also noted that the depiction of "Five Points" in the film exaggerates the level of violence and lawlessness that actually existed there.
https://www.gothamgazette.com/government/1380-is-gangs-of-new-york-historically-accurate

https://www.nationalgeographic.com/news/2003/3/oscars-gangs-of-new-york/