It will depend upon state laws and the terms of the policy of the at-fault party whether a person making a claim against the at fault person's property damage liability policy would get performance or custom parts repaired or replaced if they were damaged in an accident.
The Ohio Insurance regulator states that the selection of crash parts is determined by availability, cost and quality. When a vehicle is damaged, the insurer has an obligation to provide fair and timely claims service. The industry is obliged to make sure replacement parts are of "like kind and quality."
While other states insurance regulators only note that insurance companies do not have to specify use of original equipment manufacturers (OEM) or performance parts when repairing the vehicle. A company only has to return the vehicle to its condition before the damage.
In general an insurance company owes you repair or replacement with like kind and quality parts, not necessarily new parts. If the parts and repairs are guaranteed by the repair shop, and are in the same condition as the parts damaged, they conform to the repair requirements. If you insist on certain parts, you may have to pay the additional cost.
If you were in an accident and have had custom or aftermarket performance parts that have been damaged then you should discuss with the claims adjuster working your claim to find out if they will replace these parts with like parts or if they will only cover original parts and you will owe the difference if you want performance parts used in the repair of the car. It may help your side if you have receipts for the performance parts.
You can also contact your state's insurance regulatory body to find out what your specific state's laws are governing your situation.