A restaurants outside table and umbrella hit my car during a storm. Are they responsible?

Why would they be responsible? They can't predict the weather. You can sue anyone you want for anything - doesn't mean you'll win. Would you sue a store if a shopping cart hit your car in the parking lot?

 

You can sue.

Whether you have any chance of winning depends on factors that you have not included in your post.

The most important of which is the wind speed at the time of the accident.

Another important factor is the weight and position of the table and the umbrella.

The Phoenix area had winds gusting to 30 mph last week. Other areas may have had higher winds.

Wind speed like that could easily lift a table and an umbrella and send it sailing and it would be unpredictable and therefore no negligence so you would lose.

Most people would describe the incident as an Act of God but the legal doctrine is lack of negligence. Without negligence you don't win.

 

If my car were damaged the way yours was, I'd call my great automobile insurer and they'd make sure my car was repaired perfectly.

That comprehensive portion of any automobile insurance policy is great, especially with my ZERO deductible.

I pay others to wear my risk.

I am risk averse in all that I do.