Vote Buying is an occasional tactic in shareholder for-profit companies. Someone pays a shareholder cash for control of their votes. This is relevant because there are a fixed number of shares.

What would Vote Buying look like in a membership organization? Well, unlike shares, there's really no limit to the number of memberships. In many organizations, the memberships are of nominal cost. So the Vote Buyer could simply buy the memberships directly from the nonprofit. He'd need to have other people be the nominal holder of the memberships, who would then sign over voting rights to him.

What would happen if a Vote Buyer walked in with stack of proxies and a check for 100 memberships? Would your nonprofit permit this, or deny it?

Branford Electric Rwy. Ass'n. - Shore Line Trolley Museum requires voting in person, so the buyer would have to ensure that the bought members attended the meeting and cast their secret vote as intended.
Electric City Trolley Museum Ass'n. requires voting in person, but also allows each voter who appears in person to also cast 1 proxy vote. He could cast the proxy and withhold his own vote.
Baltimore Streetcar Museum, Pennsylvania Trolley Museum, and (I think) Northern Ohio Railway Museum allow mail voting, so it's hard to tell what happens before the envelope is sealed and mailed. Baltimore also allows proxies to be appointed, with no limit on how many each may represent.

Those are the 5 I belong to now, so I couldn't give a single answer to the poll.

All of these Museums encourage gift and family memberships. Most of them have a short waiting or processing period before applicants become new members and can vote, so I don't think that a check that arrives at the voting meeting will have the desired result. I don't know if a proxy granted before the member is able to vote is valid.