For me, its not that games with cute cartoon characters are the problem, I grew up with arcade games like Donkey Kong and pacman, very much cartoon style characters. Its the genre of game that was changing - I never really liked 3D platformers, RPG,s or action games so stuff like Mario 64, Zelda, or Banjo Kazooie just didn't appeal to me.
In general though, I have absolutely no problem with "kiddy" games but they have to fit into the genre and style of game I enjoy, which weren't found on the N64, PS1 or other consoles after the 16-bit era.
And just as an offside, I can't stand games with a lot of gore, violence or cursing either which is why most of the current gen turns me off too.