No, a credit inquiry for a car insurance quote will not affect your credit score.
Some insurance carriers do not pull or use credit as a rating factor, but most of them do. If it is not used, your credit will not be pulled.
CarInsurance.com recently added Starr Indemnity & Liability Company and they are a company that provides non-credit scored competitive rates for drivers that don't like the fact that credit is used to determine car insurance prices. Insurance credit scores are different from financial institution credit scores, but they are based upon credit history.
The company's request to obtain your credit-based insurance score will be considered a "soft inquiry". This means you will see the insurance company name listed on your credit report, but the inquiry will not influence your credit based insurance score in any way. Other inquiries from credit card companies, banks and other lenders may be considered "hard inquiries" and could influence your credit score.
As soon as carriers can find a factor that is as effective as credit to predict risk, we feel that they will move to using it instead of using credit. Credit has shown to reflect claims history in auto insurance accidents, but CarInsurance.com is concerned. Debates on using credit for insurance scoring is exacerbated by the fact that there is not much public information that verifies the relationship between credit histories and insurance claims, or why insurance premiums are priced based upon specified insurance score ranges. Public information must be disclosed to help consumer understand the correlation.