I disagree with you.
Let's start from A and ill tell you how its not sexist:
Ahri: Considering the inspiration from the Kumiho, her outfit is quite natural for luring in prey as an attractive woman.
Akali: As a ninja she wears only the most nessecary clothing and besides she never talks sturly and in most of her skins she is her skin is mostly obscured.
Anivia: You said it yourself, she is a wise eldery bird.
Annie: looks like a normal fantasy kid.
Ashe: Her clothing is very usefull due to its lightness for an Archer.
Caitlyn: Agreed, although most of her skins show her in military uniforms or with full clothing.
Cassiopeia: Is a reference to a Medusa/Gorgon, so the style is hardly attackable.
Diana: She wears full armor and has a rather strong voice and quotes that display her goals and conflicts.
Elise: As a Spider that lures people into her lair as a human i don't see your problem with her design fitting to her backstory.
Evelynn: I find her Art hardly attractive because her choice of clothing, if you can even call it like that reminds me of Voldo from Soul Calibur.
Fiora: Just dressed how its best as a duelist, light clothing that doesn't get in the way.
Irelia: Nearly full armored and and has totaly no alluring features, in all her skins her skin is completley covered.
Janna: Her design simply fits with her Wind- Mage theme, or would you like to see a floating clunk of Armor as a wind mage?
Karma: I don't think i need to explain anything here.
Katarina: An Assasin that wears light clothing, which fits her playstlye as well and on a sidenote: She mostly uses Violent quotes.
Kayle: Does not need explaination
Leblanc: While she shows a lot of skin, she looks kinda unsexy overall, but mysterious.
Leona: Heavy armor.
Lulu: Just looks like a mage
Lux: I belive her Art just makes her look beatifull instead of a ** object like you called it.
Miss Fortune: She is the only character on which i agree with you, but that's what makes her personality unique.
Morgana: While she shows a lot of skin, she was not made to look attractive overall. And a somehow more "sinful" style of dressing is fitting with the Fallen Angel theme imo.
Nami: She is a mermaid and even Ariel the little Mermaid shows more skin then her.
Nidalee: Amazon theme, that's what they look like.
Poppy: She is fully armored.
Riven: Clothed like a nomad, sounds angry, wise and desperate when talking.
Sejuani: I agree with you, i believe she should wear more armor, but since she rides on a boar she seems rather unattractive.
Shyvanna: She looks rather dangerous than attractive.
Sivir: I don't know why you would view her as a ** object, because to me she is rather displayed as a Warrior.
Sona: Have you ever seen old festivities or operas? Thats a very usual style there and since she is a musician: It simply fits her.
Soraka: She is a half Horse.
Syndra: Simply looks majestic and strong, again, would you like to see a floating clunk of metal?
Tristana: Fully Armored.
Vayne: She looks quite unattractive o.O
Vi: I don't know how you can think gigantic disproportioned robotic arms are looking sexy.