I keep hearing from people that the character of Travis Bickle in Taxi Driver was racist. I don’t see any evidence of it throughout the film. He shoots a black guy trying to rob a store but that is him standing up to crime. He never explicitly states racist opinions throughout the film.

I know one of the screenwriters said in the original screenplay, the pimp (eventually played by Harvey Keitel) was black and in the final reel shoot-out, Travis killed only blacks. But that idea was changed and the changed the race of the pimp and his goons.

The only argument I can see being made is that the film could subtlety imply prejudice when Travis talks about the crime and scum but I don’t see that as concrete evidence.

Its a character study filled with subtext, not a lot is explicitly stated as you put it.

here is an interesting video discussing Bickle's racism: