Metamorphosed means to have changed or transfigured. It may help to use those words in place of 'Metamorphosed' to get the intended meaning correct.
The quartzite found in the Santa Ana Mountains is considered one of the most pristine Paleozoic mineral deposits, believed to be metamorphosed since the deposition of the Triassic era.
(A) believed to be
This clause may want to modify the 'is considered' action, but it should also refer back to the subject of the main clause. However, the proper subject who is doing the considering, perhaps a scientist, is absent from the sentence. Unfortunately, next.
(B) and it is believed to have been
'It' can only logically be used to refer to quartzite, and 'have been' is the correct usage. Correct.
(C) and that is believed to be
'That' is such an awkward word. It clearly refers to the singular quartzite, but consider this sentence. "The leopard is one of the most beautiful cats, and that is believed to be very fuzzy." Perhaps we could say 'that animal', but just using 'that' alone as a pronoun? No.
(D) which was, it is believed,
The clause should be modifying the quartzite, not the mineral deposits, like the word 'which' indicates. Also, 'it' has no referent. This answer is out.
(E) which are believed to be
The clause should be modifying the quartzite, not the mineral deposits, like the word 'which' indicates. This answer is out.