Tyree, who was hired as the team's director of player development, said in 2011 that he would trade in his famous Super Bowl helmet catch if it would stop homosexuals from being married.
That same year, Tyree also put out a series of tweets saying, "there is no scientific evidence to support the claim of being born gay" and that he has met "former homosexuals."
According to the statement from the Human Rights Campaign, Tyree's claim "has been debunked and condemned by every major medical and mental health organization in the country, including the American Medical Association, the American Psychiatric Association, American Psychological Association, and many others."
"When did Tyree decide to be straight?" HRC president Chad Griffin asked in the statement. "The idea that someone can change their sexual orientation or gender identity is ludicrous, and the New York Giants are risking their credibility by hiring someone who publicly advocates this junk science. His opposition to basic legal equality aside, David Tyree's proselytizing of such dangerous practices goes against the positive work the Giants organization has done in recent years."
The Giants said in a statement Tuesday evening that Tyree "was expressing his personal view, and that is not the view of the Giants organization."
Tyree declined to comment on the Human Rights Campaign's statement when contacted by ESPNNewYork.com.
"I don't have any comment about it. I'm just excited to be with the Giants," Tyree said via telephone.
Tyree, who was working for the NFL, replaces fellow former Giant Charles Way, who took a job with the NFL a couple of weeks ago.
Tyree's place in Giants lore is the result of the famous "helmet catch" he made to keep alive the game-winning drive against the undefeated Patriots in Super Bowl XLII. Tyree was injured the following year in camp and never caught another NFL pass.
Giants Blasted For David Tyree Hire
Dan Graziano discusses the backlash the Giants have received after hiring of David Tyree as the director of player development..