The email itself said "you're the only person who would understand this sort of humor" so it's important to look at this in context. The recipient of the email was asian himself.
Whether it can end careers? Sure people freely ignore context and socially burn people at the stake for much less. But IRL it's important to ask whether they were actually being racist with their satire. Which I personally think is a pretty thin argument.
The author was Japanese and the subject was Filipino. There's a lot of (racial? cultural?) animus there - it's a little like a yankee making fun of a white southerner. Among Asian people, Filipino and Japanese are often considered different races.
