As long as you recognize that a release may not actually work if something untoward happens, depending on its specific wording, it is almost always better for the organization (and its insurance carrier) to have a release than not.   This is not an issue that arises only with COVID, however.

Some organizations that rely on volunteers for the implementation of their program have developed an actual form of “volunteer contract” that spells out the relationship between the organization and the volunteers. The contracts normally include an acceptance of risk by the volunteer and a release from liability of the organization in connection with the provision of service.  Many of these agreements were specifically revised during the early days of the AIDS outbreak when people were particularly afraid of becoming infected.  (See Ready Reference Page: “Volunteer Contract Can Define Commitments”) Even if you don’t want all of the other protections built into the agreement, you may want to get a specific simple release in the current situation.  Don’t think of a release as a substitute for training, however.  It is more important to reduce the risk of infection than to reduce the risk of litigation.

With members, you could ask them for a release, either as part of the request for service or as a separate document, or you could include a basic release in the membership application and/or agreement.  It is not a very friendly thing to do, but, like a release for participants in a charity run, members are likely to be willing to sign if the services are useful.  Lawyers and administrators are more likely to worry about these issues than real people.  Real people don’t normally think immediately about what can go wrong, in part because it so seldom does.