Mark Dever recently taught on the danger of a church having unconverted members. If you'd like to listen, click here. It's worth the time.
On the same subject, J.L. Reynolds wrote in 1849:
"It becomes well the disciples of the Saviour to guard well the door of admission into their fraternity. Upon their fidelity, in this respect, depend its efficiency, prosperity, and safety. An accession of nominal Christians may enlarge its numbers, but cannot augment its real strength. A Church that welcomes to the privileges of Christ's house, the unconverted, under the specious pretext of increasing the number of his followers, in reality betrays the citadel to his foes. They may glory in the multitudes that flock to their expanded gates, and exult in their brightening prospects; but the joy and the triumph will be alike transient. They have mistaken a device of the enemy for the work of God. They hailed, as they thought, an angel of light; they have received Satan. I admire and love the many sincere and zealous Christians that are found in such Churches; but I fear that this Trojan horse will finally prove their ruin."
Strong medicine from a 19th century SBC pastor, but it remains quite applicable for our time.