Based on the ancient Mayan text inscribing the sacred codes by which

BOB1993

I don't have much of a problem with the structure 'anthropologists speculate.'

Look at another example:
Based on the results of the evaluation, the committee decides how to allocate the budget.

"Based on ..." acts as an adverbial modifier. It tells us HOW the committee decides.

This is how we could use this structure in our original sentence too.

The correct tense is "were changed," not "had been changed" . There is no other action in the past after the change was made.
Also, we use "by which the Maya lived" not "by which the Maya had lived."
The changes were made at the same time as when the Maya lived. Hence we do not use past perfect for either. We should use simple past for both.

Hence (C) works best.

In some cases, using "based on" before a clause is clearly incorrect.

For example:

Based on false advertising, people have purchased inferior products.

In that sentence, nothing is "based on false advertising." Normally, the noun that follows "based on ..." would be the target of the modifier, but since "people" would not be "based on false advertising," there is no logical target for the modifier.

However, "based on ..." is not always used as a noun modifier. It has become conventional for it to be used adverbially to indicate how a decision has been made even though using "based on ..." in this was is not in line with standard rules of sentence construction.

For example;

Based on the results, they concluded that a new element had been created.

In the above example, "based on the results" is used in an unusual way to indicate how "they concluded."

So, regarding this question, we could view the opening modifier in the (B) version in two different ways.

We could decide that it has no logical target since "anthropologists" would not be "based on the ancient Mayan text." Alternatively, we could decide that "based on ..." is used to indicate how or why the anthropologists speculated.

Since it's not 100 percent clear whether that modifier is used incorrectly, our move is to find other decision points as KarishmaB outlined in the response above this one.

From the meaning POV, would it be correct to consider 'codes' similar to 'customs'?
While evaluating option C and D, I was trying to distinguish between 'codes were changed' and 'codes changed'. If codes are similar to customs, we would say 'codes changed'; wasn't very sure of 'codes were changed'. Can you help me streamline this thought?
'Codes changed' and 'Codes were changed' both would be correct?

Since we are talking about "written codes in an ancient text," we will use "codes were changed."
They did not change themselves or something else.

If we were talking about them in the sense of 'customs evolved,' then it would be fine to "customs changed over time..." meaning "customs evolved..."
But changing of some written codes will be done by someone and hence passive is required.

Why are we not using past perfect tense as in option B? Is it because "Based on the ancient Mayan text inscribing the sacred codes by which the Maya lived" is a fact?

Thanks for the detailed explanation.

I would still request one more explanation.
You mentioned, "There is no other action in the past after the change was made."

Isn't the demise of civilization happening after the change was made?

Does not it justifies the use of "Had"?