Is it because instructors, as soldiers, can't reveal their identities that they are not allowed to send photos online during military training?

Just because of the requirements of military discipline, there is nothing that can't be exposed as a soldier.

Military training

China's military training is conducted in accordance with the National Defense Law of People's Republic of China (PRC), the Education Law of the People's Republic of China, the Military Service Law of People's Republic of China (PRC), the National Defense Education Law of People's Republic of China (PRC) and the Decision of the Central Committee of People's Republic of China (PRC) on the Reform of the Education System. Military training is the basic form for students to receive national defense education, an important measure to cultivate "four haves" talents, and an extremely effective means to train and reserve our army's reserve soldiers and reserve officers and strengthen national defense forces.

The purpose of military training is to improve students' political consciousness, stimulate patriotic enthusiasm, carry forward the spirit of revolutionary heroism, cultivate the spirit of perseverance and hard struggle, enhance the concept of national defense and organizational discipline, develop a good style of study and life, and master basic military knowledge and skills.