Commissioner Wallace claims that he always has been and always will be

I would choose (A)

Here's an analysis of each option:
(A) Commissioner Wallace claims that he always has been and always will be a member of the American Civil Liberties Union. This option emphasizes the continuity of Commissioner Wallace's membership in the ACLU, both in the past and the future.
(B) Commissioner Wallace claims that he always has and always will be a member of the American Civil Liberties Union. This option is similar to option (A), but it uses "always has" instead of "always has been" to express the continuity of Commissioner Wallace's membership. To be avoided.
(C) Commissioner Wallace claims that he will always be a member of the American Civil Liberties Union. This option focuses on the future, stating that Commissioner Wallace will always be a member of the ACLU. Tense problem and change of meaning.
(D) Always having been a member of the American Civil Liberties Union, Commissioner Wallace claims that he will always continue to be so. Placement of always; the verb "having" modifies the initial idea of continuity between the past, the present, and the future.
(E) Commissioner Wallace has always been a member of the American Civil Liberties Union, and claims that he will always be. This option changes the meaning of the stem sentence.