Who are some straight characters played by gay actors, and gay characters played by straight actors?
One example that immediately comes to mind is Eric Stonestreet (straight) playing Camercon Tucker (gay) on Modern Family.
The Big Bang Theory’s Sheldon Cooper, though really more asexual than anything, is technically straight, but played by Jim Parsons, who’s gay.
Then there’s Fraiser’s Niles, Martin Crane, and Bull Dog, who were all straight, but were all played by gay actors too.
Gay actors playing straight characters:
Portia de Rossi played Lindsay on Arrested Development
Neil Patrick Harris plays Barney on How I Met Your Mother
T.R. Knight played George on Grey’s Anatomy
Kelly McGillis played straight characters in Top Gun and Witness
Sarah Paulson played Harriet on Studio 60
Zachary Quinto played Spock on Star Trek
Matt Bomer plays a straight character on White Collar and he is gay and out.
Kelly McGillis was married to men at the time of this roles. At that time I don’t think she would have considered herself a lesbian. Iirc she said it’s something she realized later.
Glee has a number of gay characters and the cast includes several gay actors, but actually does not have many gay characters played by gay actors.
Actresses Jane Lynch and Dot Marie Jones are both lesbians, but their characters (Sue Sylvester and Shannon Beiste) are straight. I have heard that Jones actually requested that her character be straight, as she felt it was too much of a stereotype to have a large and rather mannish looking gym teacher be a lesbian. Actress Naya Rivera is straight, but plays a lesbian character (Santana Lopez).
Actor Darren Criss is straight, but plays a gay character (Blaine Anderson). His straight brother was played by guest star Matt Bomer, who is gay. Neil Patrick Harris also appeared in a guest role as a straight character. A number of minor gay characters have been played by straight actors, including guest stars Brian Stokes Mitchell and Jeff Goldblum as Rachel’s two dads.
In the main cast I think the only gay actor playing a gay character is Chris Colfer as Kurt Hummel. Counting guest stars then Meredith Baxter did once appear as a lesbian character, although her girlfriend was played by Patty Duke who AFAIK is straight.
Quinto is gay?
:::: kicks personal gaydar unit :::: Man, this thing is busted. I just can’t seem to get a reliable signal out of it.
Tony Randall in Love, Sidney.
And of course, John Ritter. 
John Barrowman is gay, and plays the — for lack of a better term — “pansexual” character of Captain Jack Harkness in both Doctor Who and its spinoff, Torchwood. He also plays the apparently straight character Malcolm Merlyn in the TV show Arrow.
I read an amusing bit about how he auditioned for the role of a gay character on some TV show, but the role ended up going to a straight actor, because Barrowman didn’t seem “gay enough”. :rolleyes:
Eric McCormack - Will of “Will & Grace” - is not gay.
One that surprised me is Matthew Morrison. I could have sworn I read that he’s gay. But no - he’s straight.
You may have gotten him mixed up with Jonathan Groff (Jesse St. James), who I forgot to mention in my previous post. Groff is gay but his character on Glee is not.
A Newsweek writer caused a bit of controversy with an article that said Groff was so obviously gay that he wasn’t believable as a love interest for the Rachel character.
Probably the most famous gay playing straight roles was Rock Hudson (although he was secretly gay until he started dying of AIDS).
Robin Williams, in THE BIRDCAGE.
Although, according to The Five(ish) Doctors Reboot - Wikipedia, he has a secret wife and kids 
Brian
Justin Bartha – the guy with the least-interesting role in the HANGOVER movies – is a straight actor who played the low-key half of the gay couple on THE NEW NORMAL.
It’s an actor or actress playing a role, I think orientation wouldn’t figure into it.
I read a quote about acting from the late Sir John Gielgud:
I’m an actor, of course I can play a heterosexual!
Sean Penn, James Franco, Emile Hirsch and probably a few others in Milk.
George Carlin in Prince of Tides.
In one of the Fred Astaire/Ginger Rogers films, Edward Everett Horton’s character talks about how much the ladies liked him. Astaire says “you?” incredulously. Horton was gay, but audiences of the time probably thought Astaire was referring to his unimpressive physical appearance. In any case, his character was supposed to be taken as being straight.
The movie The Boys in the Band has several straight actors playing gay men, including Laurence Luckinbill (later Spock’s half-brother) and Cliff Gorman (Oscar nominee for Lenny).