Your child sounds completely normal. Do you remember this about being a child? Maybe you and your wife were not imaginative types–there’s a big spectrum. But really, it’s very normal, and one of the delights of being a child. Enjoy it.
I explained above why she thinks it’s wrong. She thinks other children might think our girl is weird if she keeps playing at being cats-in-danger-that-need-to-be-saved. I take it that what she worries the other kinds might find weird is not playing cats as such, more like the repetitiveness of this odd scenario.
That’s something I also wonder, why not play kittens-that-save-the-day too?
Heck we were all still doing this in grade 5. As soon as it was lunch all us girls would be Laura Ingalls and eat our lunch out of tin pails, then start running around galloping and neighing and flipping our manes. We did this pretty much ever day for the entire year.
I think we all turned out normal.
Her fantasy involves being cute and vulnerable, then being rescued by a strong, loving figure. Its the animal version of playing the damsel in distress. Kittens-saving-day doesn’t fit the narrative she enjoys.
My daughter wore mouse ears every day for two years. She decided to stop when she started first grade.
I’m going to suggest that the OP and his wife look up some general information about child development. Here are some links to get you started:
Ages & Stages: Imagine & Pretend
Pretend Play (from the "What To Expect When You’re … " series)
Psychology Today - The Need for Pretend Play in Child Development
Are you in a non-U.S. country? I can’t imagine any American nursery school discouraging imaginative play in kids that age, so I’m wondering if this is somehow a cultural thing. Regardless, if I were you, I’d have pulled my child out of that program on. the. spot.
My younger brother was a dog for so long, up until a relatively old age (9 maybe?) that (aged 16 or so) was convinced he was a Furry. As far as I know, he isn’t - he’s a perfectly normal (well, fairly normal) well-adjusted young man. Even now though, he will still occasionally snarl like a dog if I mock him for something, so perhaps he is a Furry after all - I suppose he may well choose not to discuss it with me if he is!
Slight hijack - my daughter slept with two stuffed animals (Puppy and Teddy) from age 2 all the way through high school. I stitched them up so many times that I started calling them Frankenpuppy and Frankenteddy.
When she had her first child, I went to clean their apartment while she was in the hospital. While making the bed, guess who I found next to her pillow? 
She may have made a funny face not because it’s odd or unusual, but because it’s super annoying being around (and trying to interact with) a bunch of kids who are crawling around on the floor meowing at the top of their lungs. 
My friends and I were horses too. Up to the age of 8 or so.
I play pretend games with both my kids all the time. Most of my friends do with their kids, too.
Repetitiveness won’t strike the other kids as weird. Repetitive play is the norm at that age. My five-year-old and her classmates have been playing the same pretend game at lunchtime several times a week for practically the entire school year.
What could possibly be a problem is if she’s not learning to take on other people’s games, as well as bringing her own to the mix. That’s one of the major social developments at that age: learning the process of give and take - the complicated process that leads to ‘We all played Jenny’s Cat Rescue game for a while, and then we made it Cat and Rabbit Rescue because Oscar likes being a rabbit, and then we all switched to Ellie’s Flying Superheroes game, and then the superheroes could be princesses too because Callie had her tiara in today, and then…’
If your daughter demands to stick with Cat Rescue 100% of the time, instead of learning that give and take, then yes, that could become a problem. But the problem isn’t the pretending or the repetition. It’s the lack of interplay - the refusal to allow space for anyone else’s ideas.
ETA: And even when it comes to that, she’s only at the beginning of the stage when they start learning that skill. If she still can’t take on other people’s ideas when she’s six and a half, that could get other kids seeing her as weird. At not quite five? Not a problem.
Oh, forget everything I said then…the cross-cultural stuff can be amazingly tricky to navigate. When I commented, I was just thinking about Americans in an American environment.
Although we’ve always lived abroad, I was fortunate to have enough similar-minded Western friends in both Egypt and Indonesia that I could do some reality testing with when my son was little. We all noticed that various other non-Western cultures we interacted with absolutely did not get the whole play date reciprocity thing.
Sort of an aside, but I can’t help sharing: The most breath-taking example of not understanding how playdate planning should work was a mom who used to happily arrange for her son to come over to visit with my son, on many occasions. Exactly once did she offer hospitality herself, when she took my son and his friend to a mall. In a year and a half, my son NEVER got invited to his friend’s house - not once.
Then, my son changed schools. He and the above-mentioned boy were not all that close and it was no longer convenient for them to come home together from school, plus I figured that the other family was long overdue to invite my son to their house so I certainly wasn’t going to initiate yet another visit to our house by the boy. Then his mother texted me asking me when he could come over!
I have other similar stories, but that is the one that really blew me away.
Thats what I am assuming, ideas on childhood and children can be very different outside the USA.
I can remember my wife’s nephew who was like seven at the time walking around with his eyes closed, my MIL asked him what he was doing and he said pretending to be blind. The explosion of outrage and anger by every adult present baffled me, I think his father said he later spanked him for it.
I take my four year old to a local park, and get disapproving looks from people because how dare I have a child laughing and running in circles in a wide open park. We are the only parent and child there sadly, openly been told white people are such fools with their kids.
I take him to a wealthy area with tons of foreigners with a nice playground, nice to be around people that know childhood is for fun and play instead of strict obedience and competing with other parents for the most stoic child.
Years ago as I was waiting at the post office, a little girl darted out of line and ran off. Her mom quickly retrieved her. “Mommy, I’m an arrow,” the little girl said. “Yes dear, Mommy knows. Stay with Mommy.”
This was around the time there was a circus ad on TV in which some aerialist had a “Human Arrow” act in which she was “shot” from a giant bow. I’m guessing that’s where the girl got the idea.