Yes, in fact the campaign to ban or censor offensive elements of film proved to be a consolidating moment in the history of the NAACP, which had been founded only six years before the release of the film in 1915. The NAACP sought to ban the film in Boston and other cities (the film was initially banned in the state of Ohio, partly because protests convinced Republican Governor Frank Willis and the state censorship board that the film stirred up race hatred), while organizing marches, rallies, and mass gatherings to publicize its concerns about the movie's racist message. There were protests in several cities, and in Philadelphia the protest degenerated into a race riot. The NAACP also published a pamphlet to rebut the contents of the film, which it distributed to chapters across the country, while also calling for filmmakers to counter the blockbuster's message. The organization was unable to raise the funds to make the movie, "Lincoln's Dream", but ultimately this campaign led to the production of Oscar Michaux's 1920 movie, "Within Our Gates".

The struggle against the film provided the organization with national publicity, which some have argued laid the groundwork for a dramatic increase in membership after 1918 (although the wave of lynchings and race riots that year might have been the primary cause). Yet the leaders of the NAACP were conflicted about the campaign, because it challenged the principle of free speech. As W.E.B. DuBois later put it:

In combating this film, our Association was placed in a miserable dilemma. We had to ask liberals to oppose freedom of art and expression and it was senseless for them to reply "Use this art in your own defense." The cost of picture making and the scarcity of appropriate artistic talent made any such immediate answer beyond question.

The protests had some effect: the film was banned in Ohio (although the ban was lifted following the election of a Democratic governor in 1916) and Kansas, as well as some cities. Ironically, though, the controversy also provided the film with free publicity, while also tarring the NAACP with the brush of censorship while presenting D.W. Griffith as an embattled champion of free speech. Nonetheless, the protests continued long after 1915: between 1915 and 1973, the NAACP protested showings of the film at least 120 times.

See: https://www.newyorker.com/culture/richard-brody/the-black-activist-who-fought-against-d-w-griffiths-the-birth-of-a-nation; Stephen Weinberg, "'The Birth of a Nation' and the Making of the NAACP," Journal of American Studies, Vol. 45, No. 1 (February 2011), pp. 77-93; Goodwin Berquist and James Greenwood, "Protest Against Racism: 'The Birth Of A Nation' in Ohio," Journal of the University Film Association, Vol. 26, No. 3 (1974), pp. 39-44; Paul Polgar, "Fighting Lightning with Fire: Black Boston's Battle against 'The Birth of a Nation'," Massachusetts Historical Review, Vol. 10 (2008), pp. 84-113.