Intuitively, truly open membership (without some sort of bond in form of hash power or stake) isn't possible in trustless setting, because the collateral is there to replace trust. Best you can do is self-referential PoS, and even there you need some sort of bootstrap for the self-referentiality ... to refer to.

Easiest way to get open membership is through trust DAG or hiearchy, ByteBall, Ripple and even Tor does it. But those are quite obviously not trustless. To explore that area, you might ask under what circumstances is trustlessness necessary, and to which degree optimistic trust may work. For example bittorrent or IPFS is open membership with extremely rudimentary quorum (one-to-one optimistic tit-for-tat), yet sort of "consensus" is achieved (slow leech vs honest peer uploading back will be judged quite universally). This works because the stakes for sophisticated attack are not high, it's only to prevent casual abuse.