Applying for car insurance does not hurt your credit score or credit.
When you apply for car insurance the car insurance company will check your credit score and credit history but the car insurance will only do a soft inquiry which does no harm to your credit or credit score.
However with a loan or auto loan the auto loan company or bank or lender will check your credit also but that will do a short term harm to your credit score.
So if you do apply for an auto loan or other loan then your credit score may drop a few points for around 6 months to a year.
But the hard inquiry should not harm your credit too long.
But applying for a shopping around for car insurance or other auto insurance will not harm your credit score.