Post an anime character who has an odd sense of what is cute.

At times, Rena Ryuugu from Higurashi No Naku Koro Ni.

Natsuki kinda does, except for when he calls Syo cute cause he really is cute :D

Hmm... the only character I can think of is Hakase from Nichijou; hers isn't too weird, but she thinks that robots are adorable.

Would Katsura (right) count? he think's Elizabeth (left) is cute
but in a way, she is cute :3

Kobato and Akane Tendo (they both make the weirdest, creepiest dolls and call them cute. You can't even tell what they are! Lulz, they are exactly the same in that sense.)

Elizabeth from Black Butler thought this was cute. Also, before that, she thought the one in white was cute when he was hung

Gardenia (Pokemon) fits that description quite well. In fact Gardenia even order Cacnea to aim and shoot its Pin Missiles directly at her back and she loves every minute of it in this scene. That shows her complete OBSESSION with Grass-type Pokemon overall