Then you shouldn't be a lawyer. You have a professional responsibility to defend any client your firm assigns to you, and defend them to the absolute best of your ability. If you refuse to defend a KKK member as vehemently as you would a BLM member, then you really have no business being a lawyer. Even the ACLU understands that.
That would be firm policy, not professional responsibility - and the firm could be violating its ethical rules if it assigned a client to a lawyer where it knew the lawyer had strong reservations about representing the client.
As for Professional Responsibility, here is the relevant Texas Rule for withdrawal from Representation. It is even easier to decline representation. As a solo practitioner, I will not face discipline for declining to represent a klansman. This is true, even if I take in representing every BLM client that comes along. In fact, depending on what matter I am representing a BLM client on, I may have a conflict of interest where it would be unethical for me to represent a klansman.
Rule 1.15. Declining or Terminating Representation
(a) A lawyer shall decline to represent a client or, where representation has commenced, shall withdraw, except as stated in paragraph (c), from the representation of a client, if:
(1) the representation will result in violation of Rule 3.08, other applicable rules of professional conduct or other law;
(2) the lawyer's physical, mental or psychological condition materially impairs the lawyer's fitness to represent the client; or
(3) the lawyer is discharged, with or without good cause.
(b) Except as required by paragraph (a), a lawyer shall not withdraw from representing a client unless:
(1) withdrawal can be accomplished without material adverse effect on the interests of the client;
(2) the client persists in a course of action involving the lawyer's services that the lawyer reasonably believes may be criminal or fraudulent;
(3) the client has used the lawyer's services to perpetrate a crime or fraud;
(4) a client insists upon pursuing an objective that the lawyer considers repugnant or imprudent or with which the lawyer has fundamental disagreement;
(5) the client fails substantially to fulfill an obligation to the lawyer regarding the lawyer's services, including an obligation to pay the lawyer's fee as agreed, and has been given reasonable warning that the lawyer will withdraw unless the obligation is fulfilled;
(6) the representation will result in an unreasonable financial burden on the lawyer or has been rendered unreasonably difficult by the client; or
(7) other good cause for withdrawal exists.
(c) When ordered to do so by a tribunal, a lawyer shall continue representation notwithstanding good cause for terminating the representation.
(d) Upon termination of representation, a lawyer shall take steps to the extent reasonably practicable to protect a client's interests, such as giving reasonable notice to the client, allowing time for employment