You'd have to compare the two--reality and Runeterra--before getting to the "why". There's no "racism" between humans in Runeterra, just nationalism (due to the constant warfare and clashing ideologies) and "racism" between species (Such as against Yordles, Vastayans and dragons). Sexism is fairly uncommon considering that many powerful individuals within Runeterra are female (Rift Harold, Rek'Sai (Two void superpowers), Ashe, Sejuani, Lisandra (All three of them are queens of the most dangerous locale on Runeterra), Senna (embodies a collective power through her weapon), Illaoi (cult leader), Miss Fortune (scourge of Bilgewater), Fiora (killed her father, arguably the most powerful swordsman in Demacia), Shyvana (The king's right-hand), Lux (super strong mage for no reason whatsoever), Tristana (Yordle hero), Nami (tide queen), Leblanc (leader of the Noxus Illuminati), etc; and these are just the playable ones). Finally, homophobia is all but nonexistent (I haven't combed through every piece of lore so it's possible that it exists somewhere).
Now, given that discrimination barely exists outside of the national level, that removes almost all of the psychological triggers for transgenderism on a societal level to exist. That isn't to say that it doesn't exist, because we know for a fact that it does (Speaking of Leblanc, she's known to play any role necessary. I find it wholly possible for Riot to just come out of nowhere and say that she was originally a he but throughout the centuries lost sight of his original identity. That would be incredibly interesting, and I'd love to see a Legendary skin that's a male version of Leblanc or an Ultimate skin that begins as male Leblanc but as time goes on in-game (or as abilities are leveled up) he transforms into a she, so we basically get to see Leblanc's transformation in real-time. Doesn't even have to be a full Ultimate price, maybe GGMF price (since this is just an extended idea of Pulsefire Ezreal). Hell "Leblanc" isn't even her real name so the champion name changing along the game would also be a neat idea.
Anyway, considering what we know about Runeterra vs what we know about Earth's societal histories, the existence of societal transgenderism would be incredibly improbable. There's just no reasons behind it currently.