If I want stable blood sugar and to not have extra hormones in the body, will drinking soda when I have an overall high fiber diet ruin insulin balanc?

Yes it will. Yes , soda is very bad for health , bad for other systems not just Insulin balance and blood sugar. It has high calories ( 300 ) , contain corn syrup in it has high fructose , excess of it is not good for health , even diet soda has to many chemicals , best drink is water which is free ( if you don't by bottled water ) and great for health.