In a conversation with Halsey before last weekend's match against West Brom, Taylor said the Premier League match official had told him he had received threats to "put a bullet in the heads" of him and his family.
Halsey, who recovered from throat cancer to return to refereeing in 2010, was at the centre of Twitter abuse last year after he officiated a stormy match between Liverpool and Manchester United.
The 51-year-old was left to complain to police after a user of the social networking site wrote: "I hope Mark Halsey gets cancer again and dies".
Steven Taylor: "He asked me how I felt about the Sunderland game and I said there had been no problems at all, that it was just a bit of banter.
"I didn't realise that he gets death threats and all that.
"He has had death threats to him and his family - people talking about his family, his kids, about putting a bullet in their heads.
"I didn't know that kind of thing happened. That was a bit of a shock to me, a real eye-opener.
"I asked him how he dealt with (the abuse) and he said 'You've just got to get on with it and not let it get to you'.
"But I don't know how you can shrug off something like that. That must be incredibly hard.
"I think referees deserve more credit."