I'm not sure if the death threats actually happened so much as people spewing a whole lot of vitriol at the writing team tbh. At the time I remember asking if it was true what fandom was repeating about death threats to the writers, and the quote from James Moran (the writer of said episode) was

I've received over a thousand messages from viewers talking about the show. The vast majority have been extremely positive. Even though many of them are upset, angry and shocked, they have managed to express that without making it personal...But the rest of the messages? Unacceptable. Some have been spewing insults and passive aggressive nonsense. Accusing me of deliberately trying to mislead, lie, and hurt people. Telling me I hate the fans, that I'm laughing at them, that I used them, that I'm slapping people in the face, that I've "killed" the show, that I'm a homophobe, that I want to turn the fanbase away and court new, "cooler" viewers, even that I'm hurting depressed people with dark storylines. Asking me to pass on vitriolic, hateful messages to people I love and respect.

Not cool.

So some fans obviously responded extremely badly, but I've never been sure where the talk of death threats come from. The writers have never talked about receiving any