You have two issues here, one legal and one coverage of insurance.  It is definitely permissible to have both voting and non-voting members of a nonprofit.  Our standard bylaws specifically provide permission for non-voting members.  (See Ready Reference Page: “Bylaws Function as ‘Constitution’ of Nonprofit Corporations”)

That may not solve your insurance problem, however.  I have often mentioned that I am a “member” of the local public broadcasting station and the art museum, but I don’t expect that I have insurance of any type by virtue of those contributions.

General liability insurance usually covers officers and directors (who are often volunteers) of the insured and paid staff and certain other agents.  Well-written policies will also cover volunteers for the organization, and provide coverage for the organization and the volunteers if they cause injury to third parties.  In some states you may be able to get workers’ compensation coverage for volunteer staff who get hurt if the curtain falls on them.  You probably have to have workers’ comp if you pay the stage crew.

Your problem is one that ought to be solvable by talking to a broker who understands nonprofits and theaters, without having to amend your bylaws to create non-voting memberships.  There are many insurers who provide such protection.  Nonvoting memberships are great for getting donations and creating a sense of belonging in the organization, but are generally irrelevant for insurance.