I have a world that I made up which consists of anthropomorphic cats (it's basically "very old times" but with cat people). One thing about this anthropomorphic cat world is that there's a class hierarchy based on breed/fur color (based on real-life racism and American stereotypes of cats based on fur colors and breeds). Discrimination and stereotypes based on one's breed/fur color is common, a lot of cats are very keen to keep their bloodline "pure", and inter-breed relationships are a taboo. I want to make a story about a high-class male cat who appears to be traditional and conservative, but is in a secret relationship with a cat whose breed/fur color is different from his from the lower classes because I wanted to explore the themes of breaking social norms within a very traditional, conservative society consisting of talking cats who stand on their two legs and behave like humans. The thing is: should I make this into a story? I'm scared it's gonna be one of those kind of stories where you could replace the anthropomorphic characters with humans. Also, my made up cat society functions a lot like how cats act in real life.
First off, you can replace your cats with humans because you just said you can. So, it already is "one of those kind of stories." But is that bad? It's been done before with high success. Also, you have to make a decision on how serious you want the story to be in delving into those themes.
It isn't that different from what SciFi and fantasy do in some cases. Take sensitive topics out of the context that people get irrate about, and package the topic in a way that can open minds.
Should you write the story? The question is, do you want to write the story? If you do, then go for it. Have fun, be frustrated, overcome problems in the plot, and don't ever be scared to write.
Catriona raises a good point, but left something out. Even if it turns out to be the biggest pile of crap put on paper. That is fine as long as you learn from writing it. Bad work does more to hone our skills than good, because you don't learn from not having to fix mistakes.