Getting Car Insurance Quotes will not harm or affect your credit score at all.
When you do get an auto insurance quote they will pull your credit score and an inquiry will be placed on your credit report however the inquiry will not affect your credit rating or credit score.
The inquiry will also not affect your ability to get loans, mortgages etc.
I've gotten many Insurance quotes for Auto Insurance as well as other types of Insurance and although there was an inquiry on my credit report my credit score never went down nor was it affected in any way.