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I'm seeking the word that describes a character trait for someone who, when given a system of beliefs, methods, or views, will sort through and accept or emulate only the best or purposeful parts of the system, while disregarding the irrational, superfluous, or unnecessary parts of said system.

I'm looking for adjective, used to describe the tendency of a person to act in a certain manner. I believe it ends in the suffix -ive, though I cannot be sure.

"Arya may see the purpose of their system of beliefs and the good that they do, yet she often argues at the inconsistent narratives and irrational acceptance of blind faith that such views require. She can be very ____ in matters such as these."

I'm looking for a neutral connotation.

Further context (long shot): it is used in one of the Inheritance Cycle books for one of the main characters, Eragon, to describe his love interest Arya, in a similar manner as posted above. I simply cannot find or remember the exact wording, or the chapter that it was used in, even though I have searched the definition of this word before.

A synonym for such a trait, used as a verb, would be "to cherry-pick".

e.g. "Bob likes to go to church, but when it comes to the Bible, he cherry-picks what to believe and what not to believe."

Further to a comment provided by Carly, the English adjective I'm looking for is also likely to match the Japanese concept of iitoko-dori.

The adjective selective fits your description. It ends in -ive and matches the meaning you want the word you're looking for to have. The Oxford Dictionary gives this adjective, among other meanings, the following definition:

(of a person) tending to choose carefully

Example sentence:

He is very selective in his reading.

How about 'discriminating'?

Here are some attested examples:

a. Fraternities and sororities play a huge role in the student life of many Americans who attend higher education, providing an instant network of friends, and a vast network of contacts to make use of after graduation. The most “prestigious” student groups can be very discriminating in who they admit. (The Independent)

b. Here’s what developmental psychologists do know: Boys can be very discriminating when it comes to choosing a plaything. (Slate Magazine)

c. With so many selections of golds and silvers, a scenic artist or faux-finish painter can be very discriminating when selecting a metallic finish. (Scenic Art for the Theatre: History, Tools and Techniques)

FOUND IT!

Eclectic

adjective

eclec·​tic | i-ˈklek-tik, e-

Definition of eclectic (Entry 1 of 2)

1. composed of elements drawn from various sources
   also: heterogeneous




2. selecting what appears to be best in various doctrines, methods, or styles

Note on other answers

I must apologize for the misleading "-ive" suffix that I had originally assumed that the word contained.

@Mike R - While selective does, in a broad sense, cover the grounds of the word I was looking for, it does not pertain specifically to sets of ideals. One can be selective about anything, including vocabulary and semantics. :p

@listeneva - While discriminating does fit the definition that I was looking for, I feel that it can carry a negative connotation that does not work well when describing one who accepts and emulates the best of different ideals and philosophies. Also, Slate Magazine is being a little one sided there. Girls can be just as discriminating, if not more so, for their play things. ;)