"Defender Denial" is, perhaps, an interesting subject all its own.
If baseball fans and writers call Shohei Ohtani "today's Babe Ruth", it is a compliment coming from a third party, and certainly would not be mocked. And Ohtani would feel honored. In fact, this is now fact, as this has happened many times.
If Shohei Ohtani made a practice of calling himself "today's Babe Ruth", then he would probably be the brunt of quite a bit of mocking and trash talk on the field. Would a player/players/fans get suspended/removed for calling him "Babe", being snotty brats, goading him, teasing him, trash talking him, getting in his head for his own arrogance,,,,,, even if Ohtani said he didn't like it?
I think Anderson is the only one calling himself "today's Jackie Robinson".