Changing your car insurance to a different company will not hurt your credit score.
I've changed car insurance companies a few different times and never has it affected my credit score.
When you do shop for other car insurance the insurance company will pull your credit but it won't affect your credit score since the credit check the insurance companies do is a soft inquiry.
So if you want to shop around for cheaper car insurance you can do so and change insurance companies as often as you like without harming your credit score.