Maybe it's an American term, but to me, "hate mail" is the opposite of "fan mail".
It doesn't literally imply that the sender is livid with hate, or is committing sins against charity -- "hate mail" is the kind of mail you DON'T quote in your advertisements.
The "hate" in "hate mail" is weak, I guess you could say.
I don't know where I got it from, but I thought everyone used the term. It seems to come in handy.
And the person didn't merely state "I disagree with you, and won't be buying your products."
Here is part of what they said:
...associates you with some of the most discredited and evil
enterprises of the last century...
The forcefulness of what they are saying, and HOW unhappy they are with the company, classifies this as "hate mail" in the sense I described above.
Matthew