Disclaimer: IANAL; this is not legal advice. This is a lay opinion and it may or may not be an informed or accurate one; approach it with a healthy dose of skepticism.
You're asking a technical legal question but your terminology is imprecise and inconsistent; I'll give it my best shot by interpreting the question as follows:
In the United States, is there any legal obligation for the provider of an interactive computer service to defend or indemnify against civil claims any user of that service when the user has a volunteer relationship with the provider?
Note that I have restricted the question to matters of civil claims because you seem to be specifically asking about lawsuits.
Definitions
Interactive Computer Service
In place of "organizations/communities with servers in the United States," I use the term "interactive computer service" as defined in 47 U.S.C. § 230(f):
(2) Interactive computer service
The term “interactive computer service” means any information service,
system, or access software provider that provides or enables computer
access by multiple users to a computer server, including specifically
a service or system that provides access to the Internet and such
systems operated or services offered by libraries or educational
institutions.
Volunteer
There isn't just one definition of a volunteer; much of the discussion on the subject has to do with labor law and distinguishing volunteers from contractors and employees; e.g., the definition in 29 CFR 553. That's not really applicable here; we're interested in distinguishing volunteers from regular users. I'll use the definition from 42 U.S.C. § 14505:
(6) Volunteer
The term “volunteer” means an individual performing services for a
nonprofit organization or a governmental entity who does not receive—
(A) compensation (other than reasonable reimbursement or allowance for
expenses actually incurred); or
(B) any other thing of value in lieu of compensation,
in excess of $500 per year, and such term includes a volunteer serving
as a director, officer, trustee, or direct service volunteer.
Note that the definition of a volunteer is limited in scope to situations involving certain institutions; note also the definition of "nonprofit organization" in the same section, paragraph (4).
There are almost certainly many other definitions in many other contexts; I chose these definitions because they are applicable at the federal level, and as such most closely align with the scope of your question.
Analysis
There do exist laws in some states establishing an obligation to indemnify on the part of employers toward their own employees (e.g., Cal. Labor Code § 2800) but that has nothing to do with interactive computer services or volunteers per se. While an interactive computer service can certainly be provided by an employer, and such laws may apply to volunteers when they are paid workers, you don't seem to be asking about traditional labor relationships. I've found no evidence of any U.S. law or regulation explicitly establishing any obligation to indemnify/defend on the part of an interactive computer service provider toward any other party.
In the case that a contract exists between the provider and the user, the terms of such contract would apply to the extent that the contract is enforceable. However, the "terms of service" to which users of interactive computer services are often required to agree may or may not constitute an enforceable contract. That's a whole separate issue, way beyond the scope of this question.
In the case that a contract exists between the provider and some third party, a volunteer (such as a community moderator, content contributor, or editor) could act as an agent of the provider. This is important in determining liability for actions the user may have taken in their capacity as a volunteer, but it still doesn't establish any obligation to indemnify on the part of the provider. Rather, it would determine whether the provider, the volunteer, or both are liable for the actions of the volunteer; and if both, whether the liability is joint and/or several.
Paid workers, especially those represented by labor unions, may have contractual relationships that create some obligation to indemnify or defend on the part of the employer or client organization, but that would be a separate issue. In the case that such contracts were commonplace, it would be understandable for a lay person to misinterpret the enforcement of standard contracts as indicating some general legal obligation that does not exist.
Related Reading
The following is a selection of the most related and/or interesting sources I came across in the course of researching this topic, loosely organized and in no particular order.
- On liability and online speech:
- On liability and volunteerism:
- On indemnification:
