What you describe is a later development. There was no comic code or movie censorship in the 19th century or in the centuries before, wherein lay the sources for the Grimm's tales.
Censorship and criticism of "vulgarities" I honestly think has been around since... well, since art begins. However, the exact nature of what is a vulgarity often differs from culture to culture and from time to time.
In the US, there was no comic code or movie censorship, but there was things like Comstock laws. Would Walt Whitman's "Leaves of Grass" raise many eyebrows today? It did in the 1850s-60s. (http://www.unm.edu/~unmvclib/handouts/bannedboston.pdf)
It is true that Grimm's tales were at first meant to be more of an educational archive of folklore that otherwise would have been lost. (https://www.neh.gov/humanities/2015/marchapril/feature/how-t...) However, apparently, it was found after publishing that the stories appealed to parents and children. So between the first and seventh edition, apparently the stories were made "more appropriate" for children of that era. (https://books.google.com/books?id=6gX-hNshMJEC&lpg=PR39&dq=M...) In those times, that more meant getting rid of any bawdy humor and any references to sex (violence to a "morally correct" end was okay though).
Culture changes; it seems like nowadays, some degree of bawdy humor is okay in children's entertainment. However, I've seen many articles wondering if the Grimm tales are too scary for kids.
