I remember a long time ago that there was a movie or movie series where the actor or director refused to show any blood in the movie despite there being fight scenes. Can’t seem to find any results in Google so I thought I would ask some experts
the only one I can think of is Die Hard 4. They shot it without blood and bad language to release it as a PG13 and then later for the unrated version on disc they redubbed the dialogue with some language and added blood with CGI. I'm pretty sure that's not what you're thinking of though. I think Expendables 2 was watered down in a similar way to release it as a PG13 aswell.
But, yeah, I don't think either of those are the answer you're looking for. To be honest, for decades you wouldn't see blood in pretty much anything in any genre unless it was an X rated release.