All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
The rules and regulations set by the airline companies are intended to preserve the safety of the passengers. The Muslim is required to abide by such rules and regulations for the sake of preserving the public interest. If we assumed that some of these rules serve the private interests of the airline company rather than the public interests of the passengers, then they are considered conditions between the client (passenger) and the airline company, so the client (passenger) should not violate these rules because the Prophet, sallallahu ‘alayhi wa sallam, said, "Muslims are bound by their conditions, except for a condition that declares lawful what is unlawful or declares unlawful what is lawful." [At-Tirmithi] The hadeeth means that it is incumbent on the Muslims to abide by the conditions stipulated in the contracts that they make with others.
If the airline company bans carrying food in the luggage and the passenger is aware of this and agrees to travel on their flight, this is an explicit or a tacit approval of this condition. Accordingly, he may not violate this condition.
If the questioner's parents want to carry the unauthorized food, he should clarify to them that this is not allowed and that the Islamic Shariah instructs adherence to these rules and regulations. The son should clarify this to his parents in a polite and wise manner.
Allah knows best.