In this sentence, Do this participle (from "made by ~above") modify (or qualify?) both "assumptions"?
Many people may have sympathy for some assumptions, but reject others made by those taking the two opposite positions sketched above.
If so, why do participle modify both? This sentence is from this document on page 19. The-ethics-of-research-involving-animals-full-report.pdf
In my opinion, the edited quotation is not a model of good English prose. What it means is
Many people cannot accept the entire set of assumptions made by either of the opposing sides.
As for the specifics of your question, the quoted text contains three participles, namely “made,” “taking,” and “sketched.” You did not highlight any participle. Presuming you meant “made,” it does modify a different noun and pronoun, which are separated by a conjunctio and new verb, namely “assumptions” and “others.” That is not ungrammatical, but it is hard to construe. It is a major reason why I would not recommend writing a similar sentence, but I reiterate that it is grammatical.
EDIT My answer above (made before you edited the original question) disagrees with the answer of @gotube. I should perhaps clarify my post.
As a matter of descriptive grammar, I do not believe that there is a rule saying that a relative clause (or modifying participle) can refer only to the immediately preceding noun and can never refer to multiple nouns.
Chicago and New York were cities in the United States during the nineteenth century that made major investments in infrastructure.
In the preceding sentence, “that” refers to “cities.” The century did not make investments. The sentence is not ungrammatical, at least not as a description of how those for whom English is a native language actually use the language. Nor do I believe that prescriptive grammar states that a relative clause can have only one antecedent and that that antecedent must always immediately precede the clause or modifying participle.
Where gotube and I agree is that constructions where a relative clause or modifying is far removed from its antecedent or antecedents are hard to understand and often ambiguous. If you want to be understood, separate a relative pronoun (or modifying partiple) from its antecedent or antecedents by as few words as possible. This is especially true when you have multiple antecedents or when you replace a relative clause by a participle.
As I said, the quoted sentence is not a model on how to write English. And gotube and I are, I suspect, in complete agreement on that.
The participle "made" modifies "others" only.
It is the reduced form of a relative clause:
...but reject others (that were) made by those...
The relative clause "that were made..." modifies the noun before it, "others", which means "other assumptions", in contrast with "some assumptions". So the rejected assumptions are only the ones made by "those taking the two opposite positions sketched above".
