Terraria, for something crafty-buildy with combat and very cartoony/2d blood and gore. 1-8 players.
Don't Starve Together, survival crafting in a hand-drawn Tim Burton-esque style. 2-6 players.
Awesomenauts, 3v3 fast paced competitive game in the style of Saturday morning cartoons. 3-6 players.
Deep Rock Galactic, coop shooter where you play space dwarves and shoot bugs while doing missions together. Gore may be a bit strong for your liking, but it's very stylized and only against bugs and robots. 1-4 players.
Risk of Rain 2, shooter where you try and escape a planet together with lots of different ways to play. 1-4 players.
Age of Empires 2, old school fast-paced medieval strategy game modernized with new graphics and such. 1-8 players.
Valheim, viking survival crafty buildy game in which you explore and conquer a dangerous world together. 1-10 players.
Cassette Beasts, technically not multi-player yet but they're adding it as a free update January. It's a Pokémon-esque game where you'll all be trainers in the same overworld together capturing beasts and taking down challenges together. 1-8 players when it comes out.
All of these games are rated T for teen, but it sounds more like you're opposed to M rated violence and language than T levels. They're all also insular in that this friend group doesn't need to involve other people to play together and can either play with or against each other or the computer.
Deep Rock Galactic has mtx packs but they're cosmetic, and there's a large selection of cosmetics that you can unlock within the game itself.
Risk of Rain 2 has one proper expansion, with another on its way, and no mtx.