A creature comes into play that triggers Gala Greeters's Alliance ability, which should create a tapped Treasure token BUT a replacement effect from Jinnie Fay comes into play and I decided to create a 2/2 Cat creature token with haste. Will the token enter the battlefield tapped or untapped?
The token will enter the battlefield tapped.
The Streets of New Capenna release notes contain the following ruling for Jinnie Fay (emphasis mine):
The tokens' characteristics are entirely replaced by either 2/2 green Cat creature token with haste or 3/1 green Dog creature token with vigilance. They don't have any other abilities the tokens would have been created with. Anything else specified in the effect creating the tokens (such as tapped, attacking, "That token gains haste," or "Exile that token at end of combat") still applies.