We don't have synonyms for babiism yet — it may be a rare, specialized, newly coined, or misspelled word. The closest thesaurus entries we have are babyism, babuism and babism.
(n) :
Misspelling of Bábism. [The doctrine of a pantheistical religious sect, founded in Persia in 1844 by ʻAlí Muḥammad (1820–1850), who assumed the title of Bábu'd-Dín ("Gate of the Faith"). It combines Muslim, Christian, Jewish, and Parsi elements, and forbids concubinage, polygamy, mendicancy, slave-dealing, and the use of intoxicating liquors and drugs. Precursor to Azalism and Baháʼism.]
(n) :
Misspelling of Bábism. [The doctrine of a pantheistical religious sect, founded in Persia in 1844 by ʻAlí Muḥammad (1820–1850), who assumed the title of Bábu'd-Dín ("Gate of the Faith"). It combines Muslim, Christian, Jewish, and Parsi elements, and forbids concubinage, polygamy, mendicancy, slave-dealing, and the use of intoxicating liquors and drugs. Precursor to Azalism and Baháʼism.]