Couple of false equivalencies there.
BDSM relates specifically to a type of sex act, which would make it a subject matter not appropriate to a children's game (LGBT and straight people engage in BDSM - because it's not an orientation, it's a sex act). Gayness as such is a sexual orientation and no less appropriate or 'vanilla' than straightness. Obviously, gayness and straightness both connote types of sex acts, too, but they more broadly connote sexual identity. Parents wouldn't hide their gayness or straightness from their kids, but they'd probably hide their bondage gear. If including gay relationships is too risque for this 'vanilla' family game, then including romantic relationships AT ALL is.
As for trans gender options - they're kind of built in already. As with many games where identities can be constructed, trans folks have the option of playing as a gender that may not align with their physical/birth sex. The 3DS doesn't analyze the player's genitals and force them to create a cis-gendered Mii avatar.