Board Members of an HOA

More than likely this section of the By-Laws has survived from when the Declarant/Builder was in charge and had non-members on the BOD.

1) Would this mean that a non member appointed to the board should not be there?

I know in your previous posts that there is one member of the BOD who you feel shouldn’t be on the BOD as they are not a member. Is this person a spouse of a member or someone totally on the outside of the development? If they are a spouse all they would have to do is be added to the deed to become a member. If they are from the outside the problem becomes more difficult but still doable. The problem as I see it; is that you have another two sections of the Declarations where the argument could be made that the person could serve: (bold by me)

Section 4.1 Management Body and Powers of the Association. The Association is hereby designated as the management body of the Project. The Members of the Association shall be the Owners in the Project as provided herein, and the affairs of the Association shall be managed by a Board of Directors, as more particularly set forth in the Bylaws. The initial Board shall be appointed by the incorporator(s) or its / their successor(s). Thereafter, the Directors shall be
elected as provided in the Bylaws. The Association, in its sole and absolute discretion, and as more fully set forth in its Bylaws, shall have the power and duty to perform the following acts:

Section 21.2 Powers of Board. The Board shall have all the rights and powers of the Association as they are delineated in this Declaration and as are further provided in the Bylaws of the Association.

2) Should that Board Member resign or asked to step down?

You could but that doesn’t mean they will.

3) Who's responsible for allowing this to happen?

Anyone either member or BOD who knows this person’s status and does nothing; HOWEVER your Declarations also provide:

Section 10.1 Enforcement. Declarant, Merchant Builder, the Association, and any Owner shall have the right, but not the obligation, to enforce by any proceeding at law or in equity, all restrictions, conditions, covenants and reservations now or hereafter imposed by the provisions of this Declaration. Failure by Declarant, Merchant Builder, the Association or any Owner to
enforce any covenants or restrictions herein contained, shall, in no event, be deemed a waiver of the right to do so thereafter.

The limitations, restrictions, conditions and covenants set forth in this Declaration constitute a general scheme for (i) the maintenance, protection and enhancement of the value of the Project and (ii) the benefit of all Owners. Said limitations, restrictions, conditions and covenants are and shall be covenants running with the land or equitable servitudes, as the case may be. Each remedy provided for in this Declaration shall be cumulative and not exclusive.
The result of, or condition caused by, any violation of any of the provisions of this Declaration is and shall be a nuisance, and every remedy in law or equity now or hereafter available against public or private - nuisance may be exercised by any person affected thereby. Any of the foregoing to the contrary notwithstanding, no action to enforce this Declaration shall be instituted unless and until a written notice of such breach setting forth the facts of such breach has been delivered by certified mail to the Owner of such Residential Unit. In the event the
Association or any Owner(s), should commence litigation to enforce any of the provisions of this Declaration, that party, if he should prevail, shall be entitled to have judgment against and recover from any defendant in such litigation, such attorneys' fees (other than nominal) as the court may adjudge reasonable and proper.

If you want to formally question this person’s right to be a member of the BOD you have the right both in your CC&R’s and CA law to go to arbitration on the matter.