1940: Judith Anderson in Rebecca
1955: Sal Mineo in Rebel without a Cause
1958: Paul Newman in Cat on a Hot Tin Roof
1968: Daniel Massey in Star!
1969: Dustin Hoffman in Midnight Cowboy
1969: Jon Voight in Midnight Cowboy
1971: Peter Finch in Sunday, Bloody Sunday
1975: Al Pacino in Dog Day Afternoon
1975: Chris Sarandon in Dog Day Afternoon
1982: John Lithgow in The World According to Garp
1983: Cher in Silkwood
1985: Margaret Avery in The Color Purple
1985: Whoopi Goldberg in The Color Purple
1985: William Hurt in Kiss of the Spider Woman
1990: Bruce Davison in Longtime Companion
1991: Tommy Lee Jones in JFK
1992: Jaye Davidson in The Crying Game
1993: Tom Hanks in Philadelphia
1997: Greg Kinnear in As Good As It Gets
1998: Ian McKellen in Gods and Monsters
1999: Angelina Jolie in Girl, Interrupted
1999: Chloe Sevigny in Boys Don't Cry
1999: Hilary Swank in Boys Don't Cry
2000: Javier Bardem in Before Night Falls
2000: Geoffrey Rush in Quills
2002: Ed Harris in The Hours
2002: Salma Hayek in Frida
2002: Nicole Kidman in The Hours
2002: Julianne Moore in The Hours
2003: Charlize Theron in Monster
2005: Philip Seymour Hoffman in Capote
2005: Heath Ledger in Brokeback Mountain
2005: Felicity Huffman in Transamerica
2005: Jake Gyllenhaal in Brokeback Mountain
2006: Judi Dench in Notes on a Scandal
2008: Penelope Cruz in Vicky Cristina Barcelona
2008: Sean Penn in Milk
Those are all gay, bisexual, or transgendered characters that were nominated.