According to the US Government, they are but it's not always the case. It depends on the airline and its regulations. I highly recommend you before booking your flight checking the airline's policies.
Strollers, umbrella-strollers, baby carriers, car and booster seats and backpacks must be screened by X-ray. Place items in the stroller pockets or baskets, in a carry-on bag or on the X-ray belt for screening.
Standard strollers, folding wagons, and car seats can be used to get to your gate and then checked for free. They'll be returned to you on arrival. Collapsible strollers can be stored in-cabin. Car seats can be used onboard your flight too.
Airlines are technically not responsible for damage to checked car seats (or strollers either) under their contracts of carriage. This is why it is so important not to fly with expensive baby gear! As with many things in air travel, however, employees do have some flexibility to address grievances.
If you have experienced a loss or damage to your property and you feel that this loss or damage occurred as a direct result of negligence by a TSA employee, you may file a claim with TSA. If you feel the loss or damage was due to the negligence of your air carrier, please file a claim directly with the air carrier.