You couldn’t implement this policy now because the vaccine is not generally available in your area.  Even when it is, I doubt that there will be mandates requiring people to get vaccinated or denying services to them if they don’t.  And while you may want to implement a vaccine requirement when it is available for all (assuming you can determine when that date actually arrives), you may not want to require it on an absolute basis. 

The legal analysis is different based on the role the individuals play within your organization.  For employees, assuming they are at-will employees and not unionized, you can generally impose whatever requirements you wish.  If you have enough employees to be covered by anti-discrimination laws, you can’t discriminate on the basis of religion and probably couldn’t fire anyone who has a sincere religious belief against vaccination.  Your diversity, equity and inclusion goals would be jeopardized by terminating a black employee who has a legitimate fear because of the historical treatment of blacks by the medical establishment.  And what about the person for whom the vaccine is not recommended because of a likely adverse reaction?  Even if you are not covered by anti-discrimination laws, do you really want to fire individuals who don’t get the vaccine for these reasons?

Volunteers are generally not protected under anti-discrimination laws, but the same ethical questions apply. 

Members raise some additional issues.  My favorite question about nonprofits is: whose organization is it?  Do their dues give the members rights to the benefits you have promised? Even if a majority would support a general no service policy, are you going to give back some or all of the dues of those who don’t get vaccinated?  Can you afford to give rebates to those to whom you deny member benefits?  Can you afford to lose their dues in future years?

Would you deny services to a home-bound member who can’t get someone to come to the house to provide the vaccination?  One of your services is to drive members to medical appointments.  Would you refuse to drive a member to an appointment to get a vaccination?

The rest of the world will be living for a long time with the risks of dealing with persons who haven’t received a vaccination.  While you may want to encourage vaccinations, and perhaps ask for disclosure so people on both sides of the relationship will know what they are dealing with, I would not recommend an absolute policy such as you suggest.  With the tremendous interest in the vaccine among your constituents, I doubt that a whole lot will fail to get it when they can.  I would rely on the staff, volunteers, and members, understanding the situation in front of them if they ask, to make their own judgments on the risks that they are willing to take, as they have been doing for nearly a year and will continue to do as we approach a new normal over the next few years.  They will need to deal with the same questions in other areas of their lives.