I think we should less worried about people believing deep-fakes are real and more worried that politicians (and others) will be able to claim things which they actually said are deep fakes.
In both cases, though, the solution would be to find a way to allow people to tell deepfakes from real videos. For instance by having some sort of certificate provider agencies digitally sign them.
This would still make it hard to tell a deepfake from an unsigned video, of course.