The state religion of ancient China, which came into existence at least as far back as the Han Dynasty (206 B.C. to A.D. 220) and perhaps as early as the Western Zhou Dynasty (1050 B.C. to 771 B.C.), allowed
only emperors performing the ritual worship of heaven, perceiving them as special links between the earthly and celestial realms.
A. only emperors
performing the ritual worship of heaven, perceiving them as
Wrong. idiom:
allow X doing Y <-- wrong.
B. only emperors to perform the ritual worship of heaven, with the perception of them
beingWrong. "being" is wrong.
C. the ritual worship of heaven to be performed only by emperors, who were perceived as
Correct. Idiom:
allow X to be done by Y (original: allow X to do Y)
D. the ritual worship of heaven,
performed by emperors only, with the perception of them as
Wrong. The red part should be a main verb, not modifier.
E. the ritual worship of heaven
as performed by emperors only, who were perceived to be
Wrong. Idiom:
allow X as done .... <-- wrong.
Hope it helps.