If a deed is in the name of a church organization. Can a family member of the organization sell the property?

No.  A religious corporation must do a special type of court proceeding to sell the property.

Absolutely not. A church is not only a not for profit organization, it is also a benevolent association subject to New York law. As such it is required to follow the church by-laws for such a sale which must be approved by a vote of the board of directors or trustees, made to a buyer for market value and the proceeds used for the benefit of the congregation. The board has a fiduciary obligation to the congregation to get the maximum profit. If you feel the church has not followed the law you may be able to stop or reverse the sale and investigate by getting a court order. The church could ultimately lose its tax exempt status if laws have been broken and individuals have profited.