Before Photoshop, people believed in manipulated static images (as seen by all the fake UFO "photographs"). After Photoshop, it required "video evidence" to make people believe in UFOs again. Once it's possible to easily fake video material, the same will happen as with doctored static images. People will stop believing in video without additional evidence that the video is actually real.
PS: People being manipulated by propaganda is really old news. The only thing that the internet has changed is that all the village idiots who easily fall for propaganda discovered that each village has its idiot and they started to communicate and coordinate. But that's unrelated to deep fake and was already a problem before.
ok well once you don't believe in video evidence or photographic evidence then there is no evidence that could convince you of something other than actually experiencing it yourself. In which case people will just believe what they want to believe.
Usually there are other witnesses, other video sources. The more material exists, the harder it is to make the fake believable. You have to consider the sources. Who published the video, what are their motivations, who pays them.
Really, that's "internet user 101", I can't believe we're having such a discussion on HN :)
I'll give you one decent example from recent popular media: Sandy Hooks. Alex Jones didn't even need a deep fake to convince people.