Syncretism

Vietnamese folk religion is closely tied to Buddhism, Daoism and Confucianism lending many aspects (think Daoist cosmology and harmony, Confucian family values and the Buddhist concept of karma) fusing them with traditionally Vietnamese customs and beliefs. Vietnamese folk religion uses the Three Teachings (Tam Giáo), those being the three schools of thought I mentioned up top.

China

Before the 1000 year long Chinese rule over Vietnam, Vietnamese spirituality was already a fully-fledged out belief system with nature worship (belief in the spirits that live in natural entities), female diety cults (the goddess mothers) and shaman culture (communication with spirits). When the Chinese came along, Vietnamese elite began to selectively adapt certain parts of Confucianism, Daoism and Buddhism by using the already in-place foundation and adding foreign aspects onto it.

Reasons for this

They did this so they could appear as a civilized society from the Chinese perspective (anyone with non-Chinese ideals/culture was seen as barbaric by the Chinese elite) and turn Chinese ideas into their own. For example, the Lý Dynasty which lasted from 1009-1225 who accepted the Song dynasty as their overlord (for a time, Lý eventually broke off) had Buddhism as official state religion whilst blending it with local, traditionally Vietnamese spirit cults.

Buddhism

Buddhism specifically became popular in Vietnam through China and India, the sects of Mahayana and Zen Buddhism in particular. Buddhist monks saw the rituals the Vietnamese were performing and gave them new Buddhist interpretations aswell as bodhisattvas (people who can reach nirvana but doesn't so they can help others achieve nirvana) replaced some local dieties in some folk tales.

Taoism

Taoism entered through China and brought its magic practices with it, particularly its village healers who mixed alchemy and medicine aswell as Vietnamese imperial courts adopting some rituals that Chinese emperors were also doing.

Confucianism

Confucianism was China's state ideology, and when it conquered Vietnam China imposed Confucianism on Vietnam too. Vietnamese society used ancestor worship to prevent total erasure of Vietnamese culture, using their lineages as proof of Vietnamese heritage and repurposing some Confucian aspects like Vietnamese imperial cults using Confucian rituals to give legitimacy to Vietnamese rulers.

Christianity

With the arrival of the French colonial period, Vietnam saw a rise in Christianity as France actively tried to convert Vietnam to Christianity (with varying success) with the side effect of some Christian practices fusing with Vietnamese ones, for example in some areas Virgin Mary statues being placed alongside spirit statues or Western medicine being used alongside folk healing or Christian prayers being mixed with spirit medium chants.