IMO A:

since "Béla Bartók’s" music is being compared so D and E are out. Also "it" is required at the end so B is out.

If you add the missing ellipsis it looks like this.
Even though Béla Bartók’s music has proved less popular than Igor Stravinsky’s music has and less influential than Arnold Schonberg’s music has , it is no less important.

"is" is the not the verb used here so C is wrong. Hope this helps.

Vinayak

Clear enough...

IMO A
"music" is being compared, so "he" in b and d are clearly wrong. Also, e wrongly compares Béla Bartók's music with Stravinsky and not with Stravinsky's music, so it is wrong comparison.

What is the issue with C? It actually changes the tense from "has proved" (Present Perfect) to "is" (Simple Present). The intent of the sentence is to convey how music of each of the three musicians "has proved".

Perhaps an acceptable construction would have bee:

Even though Béla Bartók's music is less popular than Igor Stravinsky's is and less influential than Arnold Schonberg's is, it is no less important.