I think it has more to do with how someone identifies their personality rather than their sexuality. People like to play as characters they can identify with. In games where characters don't have different traits, or the traits don't influence gameplay as much, such as Mario Party or Mario Kart, I like to choose characters with personalities I like.
For example, I am a straight male, but I identify with more feminine personality traits than masculine. I lean more to the emotional and soft, which is generally thought to be more feminine than masculine. In Smash for me its more about playstyles that fit me moreso the emotional connection between me and the character. But in Mario games I like to play as characters like Boo, or Shy Guy, or Luigi that fit my personality, even though they are all identified as males, it is more the emotion and personality from the characters that attracts me. And in Smash when I play as a gender-swapping character I always chose female Robin, female Corrin, and female Wii Fit Trainer.
In general when it comes to character selection and gender, I think its more about who you can identify with, rather than your sexual orientation, and how the character "feels" in your mind. For example one of my Smash 4 mains is Villager, and I pick the standard male villager. I pick him firstly because I love his playstyle, but I pick his standard costume because that specific Villager just "feels" the way I feel about myself. He's a guy, but he's not a super masculine character, and his play style also suits my personality too.
When it comes to picking a character, and character attributes are ignored, I believe that being able to see yourself in the character is the key to choosing that character.