I'm not sure that "celebrity" is exactly the right word...
I am too young to remember much about the G.H.W. Bush presidency... most of what I know about him is shaped by the lens of history. I think history remembers him pretty well, especially with his son lowering the bar and Dolt 45 setting the bar so low that they'll need a backhoe excavator to find it. I think Bush the former's handling of the Iraq invasion of Kuwait set an example for countries to follow. He said that he did not go to Baghdad or remove Saddam from power because if you went to Baghdad there was no way out. Bush the latter proved Bush the former was correct about that.
I also remember reading the theory that people remember G.H.W being more likeable than he actually was because of Dana Carvey. Dana Carvey's SNL impression of Bush was a kindly old grandfatherly type who people somehow just liked, while the real GHWB wasn't nearly so affable.
I also recall George HW Bush's guest appearance on The Simpsons, and his backing vocals on this song by Ministry:
https://www.youtube.com/watch?v=imqvLToWH7k"What we are looking at is Good and Evil, Right and Wrong."
-k