Bitcoin membership is the fact of being a member of a group that gave up their ownership in exchange for digital or paper bitcoin certificates which grant zero ownership rights. Hence, there is no better word for this than membership.
Gave up their ownership? It's literally just a change of what asset they have ownership in. From the ownership of fiat, to ownership of bitcoin. You could use that "membership" argument with literally almost anything.
Sure that Bitcoin is a property if a dozen of memory bytes or paper is a property. By certificate I mean paper that verifies the fact that you own property. Gold is property, while a gold certificate is a paper that verifies the existence of this property and displays its quantity and other info.
That's actually one of the strengths of bitcoin. To prove ownership you don't need a printed piece of paper. Instead, you prove ownership by signing messages using certain addresses, or by making a certain transaction.
Yes they gave up their ownership. Either of entitlements (rights to non-monetary repayments in the case of FIAT for e.g.) or need-satisfying goods, commodities, etc. After that, they only have membership. This membership grants zero entitlements, it grants zero ownership rights, and the only way they can benefit is if new investor voluntarily transfers his/her ownership to them by entering into the scheme - which is exactly how classical fraudulent schemes operate.
Regarding the last paragraph, you talk nonsense. As a Bitcoin holder you own nothing. Bitcoin is a certificate that proves membership not ownership. Dollar is a certificate that proves ownership - of rights to non-monetary repayments. A bond is a certificate that proves ownership - of rights to interest (the coupon) and to repayment of the principal at the maturity date. A stock is a certificate that proves ownership - of rights to a share in a company's profitability or liquidation value. Bitcoin is not such certificate, it proves zero ownership rights. It is just a digital (sometimes paper) certificate of membership in a modern-day fraudulent scheme.