In a lot of old (1920s) movies there seems to be no problem with naked women. Compared to the later film industry in the 50s this seems surprising. When and why did this change and was there a campaign against it from conservatives?
Hi, hopefully someone can tackle your title question, but as to the "when and why did this change", look no further than the US film industry censorship known as the Motion Picture Production (aka "Hays") Code. Check this out:
When did it become acceptable for movies to have nudity, graphic violence, and profanity? - featuring a now-deleted username, and links to a few more on film censorship
Example: vulgar language In both "The Great Escape" and "Bridge Over the River Kwai", whistling seemed to be very important to troop morale. Is this historically documented? featuring /u/CelticJoe
Example: sleeping arrangements When did western couples start sleeping in the same bed? featuring /u/impendingwardrobe
Slightly off-topic, but here's more on the Comics Code
The simple answer is that "sex sells" (as does violence and other envelope-pushing activity).
Starting in the early 20s there was a more organized movement to "clean up" motion pictures. Will Hays (whose name became synonymous with the code - "Hays Code") was hired in '22 to head up the development of the Motion Picture Production Code
the code era was '30-'68 (though the code wasn't really enforced until '34)(due to the recent switch to sound, most movies known as "pre-code" (due to their salacious content) were produced '30-'33)
the interplay between the major studios and the code - and the enforcement of it - is due in large part to fears of actual government regulation.
Yes, movies of the silent era - up to '34 can be quite surprising in their content - and subject matter - compared to the 50s.
(it is important to note that independent studios were not subject to the code - and throughout all of screen history there have been movies of every kind of content - often shown widely)
It's just my opinion, but the code was in some ways a good thing. Things are pretty wild and the medium is still taking shape (we accept ~100min as a standard running time average - but that was still evolving through the 20s). I think it made people have to try harder and be smarter - to imply things (double entendre, etc) - to code things (cigarettes representing sex, for example)
a interesting other issue "pre code" is the widespread depiction of alcohol use during prohibition. One has to be paying attention to the year of the movie to realize that when they nonchalantly bring out a cart of drinks at the dinner party the judge and mayor are invited to - that they are all flouting the law ('20-'33)