Why was it so important that the others not find out that Kit is a girl?

If you are referring to people not discovering that Kit is a girl while traveling with the theatre troupe... it is because girls are not allowed to be actors... she would have been removed immediately.

I didn’t answer for a few moments. She was right on one point - if the others found out she was a girl, it would be the finish of her acting. She would be pushed away behind the scenes with Mrs Desmond, with nothing more important to do than stitching and darning costumes. There would have been a fearful scandal if any of our audiences had realized that we had brought a young girl on to the public stage.