Significance of the cat?

I think the cat was there in order for the scene with the cat eating the bird to take place. The bird getting killed was symbolic of the bird cage that tipped over when the father was...... with the two women when Alison walked in. Remember, ALison goes up the stairs to investigate just as she did when she walked in on her father and the party. When she goes up the stairs, she does she the father and the two women.

Because the cat was likely named Beelzebubbles or Pyewacket or something, and that sounds faintly demonic. The actual cat-actor, however, was a staunch atheist named Freddington Furrypaws, or 'Freddy' for short.

I believe there is a certain significance to the cat.
Black and White Cat.... Black and White Cake....
There is a thread going through this film. Black and white. Good and evil.
While watching this movie again yesterday I noted the clothing that the characters wore in many scenes. The one scene that struck me was when Michael comes home from a night away and Allison's friend, Jennifer is there staying with her. At first she doesn't trust Michael but Michael begs her to stay with Allison again. She realizes that Michael is really worried. I noticed that Michael is wearing all black and Jennifer is wearing all white in that scene.
When Allison goes out for a walk and ends up at the church she is wearing a black and white dress. She also wears a white dress when she arrives at Jennifer's party that final night.
There may be other scenes as well. I'd have to go back and look again.
these are just my observations But it makes sense to me.
In any case, the cat's birthday party got Allison into Chasen's apartment where she met all of these evil characters. That helped to move the story along.

"Fasten your seatbelts. It's going to be a bumpy night"

I assumed it was Chazen's familiar.

The birthday party for the cat was my favorite part. I had a black and white cat when I first saw the movie too.

Black and white cat, black and white cake.