Is it possible to play 2 of a kind or 3 of a kind while I'm blinded by the Curse of the Cat Butt?
When playing blind, you can only play one card at a time.
Curse of the Cat Butt is a clone/replacement of Blind as a Bat and follows the same rules.
Blind as a Bat instructions:

any cards must be played blind (pick one blindly, and place it face up on the Discard pile).

The expression of the Curse of the Cat Butt rules/instructions tried to clarify some points but ended up with this one point muddled. It's still kinda in there, though:

On their turn, if the blind player decides to play any cards, those cards must be picked randomly and played face up on the Discard Pile. If the card is playable, play as normal.

The way to reconcile the shift from plural to singular is to read it like Blind as a Bat:
Cards are played to the discard pile, and each time, if the card (singular) is playable, ...