One thing I've noticed in old movies that feature pro wrestlers is that there's little to no indication that the people in the movie world think wrestling is fake. Is this just for the sake of the plot or were there huge numbers of wrestling fans that thought the fights were real? If so when and why did that myth disappear so suddenly?
This is a complicated question because "people" covers, well, everyone. In the late 19th/early 20th century there were already plenty of allegations that wrestling matches were fixed, which many were, although there were some "shoot" matches into the 1920s/30s.
In 1912, French wrestler Paul Pons wrote a book where he openly discussed pro wrestling as a work, but I have no idea how widely it was read. I think it was only in French, and I never heard of it until recently when French/Quebecois wrestling historian Pat Laprade wrote about Pons for his Wrestling Observer Newsletter Hall of Fame induction. Can confirm that the book exists, though.
In 1934, a disgruntled wrestling promoter named Jack Pfefer exposed the wrestling business through the New York Daily Mail. It didn't have much effect other than to further diminish Pfefer's reputation in the wrestling business. The New York State Athletic Commission had already ruled that pro wrestling matches were "exhibitions" and could not be billed as competitive matches without special permission from the commission.
It was always public knowledge that pro wrestling wasn't strictly on the up and up. That said, there were absolutely people who believed with all of their hearts that wrestling was real into the 1980s/90s in some parts of the country, especially the rural South and Appalachia. Here's a clip of wrestling legend Terry Funk reminiscing about fans in the South trying to kill him. Wrestling villains (heels) took great pride in their ability to enrage the crowd, and some old timers lament that nobody gets real "heat" anymore.
Vince McMahon's WWF became a national phenomenon in the mid 1980s. In 1989, he went before the New Jersey State Senate and testified that pro wrestling was "sports entertainment" rather than real sport because the state athletic commission in New Jersey and other states taxed the profits of sporting events. That's typically pointed to as the moment that the myth disappeared, so to speak.
Most of this is pulled from an essay I wrote. You can read the essay and see the citations here.