Probably not much. People have believed BS forever, and mistrusted actual facts for just as long. Deepfakes are just another tool BS-slingers have in their box of dickish tricks.
There are measures to detect deepfakes, like asking a person to turn their head sideways. I opened a branchless neobank account here in the EU and part of the signup required me to turn my head sideways so that they could prove the video was not a deepfake. It's really an arms race.