Make President Diem even more hostile to Cao Dai than to Buddhists. Caodaists lead a mass anti-Diem protest/riot, which is mowed down by Diem's thugs. A Caodaist leader burns himself, which is caught by US cameraman and is spread around the world.
Exactly as IOTL, Diem is assassinated, and a succession of weak, corrupt, and incompetent rulers follow. These rulers partially rectified Diem's mistake and co-opt Buddhist clergy. Especially among the urban middle class who resent both the RVN regime and the Viet Cong, Cao Dai proliferates.
By the early 1970s, 20% of South Vietnam practices Cao Dai. After Saigon falls, it is banned due to its anti-communist leanings. It continues underground, with at least 25% of former South Vietnamese practicing it in some form.
When Vietnam begins economic reforms in the 1990s, restrictions on it are relaxed; the government feels a national religion is easier to co-opt and manage than something foreign like Catholicism, and many Communist Party leaders are rumoured to practice it. The Party does nothing to dissuade these rumours.
It's estimated 20% of Vietnamese are adherents. However, since it becomes a cultural marker of the urban middle class, its influence is disproportionately visible.
This story has parallels with South Korea over the same period, which really was a Christian-wank.
