I just discovered the very entertaining Bryan Ferry cover of “It’s My Party”. One thing stuck out: although the Lesley Gore original is clearly written from a female perspective, Ferry refuses to change the gender of the song. What other songs do this? Is it just to stand out, or is it ever done to change the meaning of the song?
Joan Jett’s Crimson and Clover has her singing about a woman.
Jack White’s “Jolene”.
Same with A.C.D.C.
Cam Clarke, a gay voice actor and singer, about a decade or so ago, released an album of love songs originally sung by women, without changing the gender of the subject of the song, because he wanted to sing them as gay love songs.
Me’Shell NdegeOcello’s Who Is He And What Is He To You.
Love both versions of this song.
Because I’m only just beginning to realize I’m an old fogey and younguns may not be familiar with the original, here’s Bill Wither’s version.
Does Joan Baez singing that Virgil Caine is her name count?
How about Lyle Lovett singing “Stand By Your Man”?
Linda Ronstadt, in her Stone Poneys days, covered Michael Nesmith’s Different Drum.
While she did adjust the gender, she left alone the line that indicates that the boy is ‘pretty’.
ETA: And there is your earworm for the day. 
mmm
The most puzzling cover of this type I can think of is Anya Marina’s cover of Ti’s “Whatever You Like” because she doesn’t remove the lines towards the end that are clearly about Ti’s penis.
An enormous amount of Spanish language covers and even originals. The writers of every Mecano song are two brothers; the singer, a woman. The singer is perceived as a narrator, they don’t need to match the gender of the character they’re singing.
Ola Belle Reed, “Bonaparte’s Retreat”.
It is a traditional folk song, so I don’t think I am breaking any rules posting all the lyrics:
I always found The Pastels’ version to be the superior one. Then again, The Pastels pretty much can do no wrong.
When The Pogues covered the traditional “I’m a Man You Don’t Meet Everyday,” they had Cait O’Riordan do the vocals.
I thought about that, but the song is not gender specific – it’s advice to a woman, but could be given by either a man or a woman.
The amazingly great guitar player Michael Hedges liked to do some quirky covers and make them his own. His version of Buffalo Stance did not change the genders.
Damn I miss him. I’m glad I got to see him live.
Ed Sheeran’s cover of Be My Husband.
I prefer the acoustic by Susannah Hoffs and Matthew Sweet.
The AV Club has bands come in and cover other bands. The Promise Ring does a fantastic cover of Adele’s “Rumour Has It” without changing gender.
I like to think that the artists are singing the song for the love of the song.
Not related to switching genders, but I recently saw the “Experience Hendrix” tour where a bunch of musicians performed old Hendrix songs. Near the end Buddy Guy came out and played a song (not Hendrix) with some rather odd lyrics, and he stopped singing for a second and said “Hey I’m just singin’ it, I didn’t write the fuckin’ thing”
Ringo Starr and The Beatles singing “Boys.”
Alison Moyet covered “Whispering Your Name” by Jules Shear and didn’t change the pronouns, turning it into a lesbian love triangle.