The historic Blair House, in Washington DC, and the Schloss Mesburg in Brandenburg have the peculiar distinction
of being recognized historical landmarks that must also function as active state guest houses for dignitaries visiting America and Germany respectively.
(A) of being recognized historical landmarks that must also function as active state guest houses
This option uses 'being recognized" here which is not making sense of the intended meaning. The peculiar distinction is 'these landmarks must serve as guest houses' and not 'being recognized as historical landmarks'.
INCORRECT(B) of recognized historical landmarks that must also function like active state guest houses
The use of relative pronoun that after landmarks is wrong as it alters the intended meaning. This option means that landmarks must serve as state guest houses.
INCORRECT(C) that they are recognized historical landmarks that must function like state guest houses
Similar to Option B, wrong use of relative pronoun and the linking of distinction to the recognition.
INCORRECT(D) that, as recognized historical landmarks, they must also function like active state guest houses
Correct use of relative pronoun with correct liking of distinction to the recognition.
CORRECT(E) to be a recognized historical landmark that must also function as an active state guest house
To be a recognized historical landmark is singular, but it's referring to two landmarks. The sentence needs a plural form to match the subject.
INCORRECTOption D is the right answer.