Should the BOT intercede when a Committee Chair rejects a residents membership due to obvious personal animus.

We need some more information. What kind of "membership" are you referring to? Committee? Other?

Assuming we're talking about committee membership, here's some general information that may help you answer your own question:

* Committees operate under the direction of the board - they have no independent authority of their own (with some pretty uncommon exceptions, which your bylaws would spell out if they exist).

* Boards can appoint or remove committee members with or without cause. The board is the final word on this.

* It's appropriate to have requirements for participation, and to ignore any applications that don't follow these requirements. In addition, committees should have charters that describe what they're supposed to be doing and how they should be doing it. Committees that aren't effectively managed will cause more problems than they'll solve.

* It's also important for board members, officers, and committee members to be able to work effectively with others. If someone does not get along well with others, it's reasonable to tell this person "thank you for your service" and appoint someone else.

Obviously I don't know the individuals involved, but as a board member I would not want to deal with anyone who will be creating drama instead of doing their job. That applies to everyone, newbies and experienced folks alike. As I mentioned above, boards can appoint or dismiss anyone for any reason - a person's inability to work effectively with others is a deal breaker in my book.

Thank you for your responseWe are talking about committeemembership
The applicant worked with four of the members in the past including three years, two as committee secretary with the committee Chairman without incident. 2 other members of the committee have no prior experience with the applicant and I believe don't even know each. The former Trustee obviouslyy has a history with the appliant.
The applicant served for 10 years on the committee 3 as Chair as well as two years on another committee as chair.
I negelected to mention the spouse of the former Trustee is now on the Board of Trustees.
Should the Board position be
My opinion is if the former trustee on the committee can not set their personal issues aside that person should resign

The Board of Trustees has the lawful right to appoint anyone it wants to the committee, for any reason it wants. The BOT can also dismiss anyone it wants. If the BOT does not like the committee chair, the BOT can dismiss the committee chair from the committee; or the BOT can state that it will appoint the chair.

That's the law. The rest of your questions are more ethical/moral/subjective/political.

In general, the Board also appoints the committee chair. The Committee often recs who they ant as chair and I think Boards do usually agree with the committee. but they are not retired to.

I agree.