Scripture presents the church as the primary institution established by Christ for the nurturing of believers and the proclamation of the gospel. In Matthew 16:18, Jesus declares, “I will build my church, and the gates of hell shall not prevail against it” (ESV). The Greek word ekklēsia (“church”) refers to the called-out assembly of believers, under Christ's authority.
A Bible study group composed of church members is an extension of the church’s ministry, not an independent entity. Ephesians 4:11-12 states that Christ gave “pastors and teachers, to equip the saints for the work of ministry, for building up the body of Christ.” The local church, through its elders, is responsible for equipping members, including those in Bible studies, to ensure doctrinal fidelity and spiritual growth.
Scripture assigns elders (or pastors) the role of overseeing the flock and guarding sound doctrine. Acts 20:28 instructs elders to “care for the church of God, which he obtained with his own blood,” and 1 Timothy 3:2 requires them to be “able to teacb". (“overseer”) in Titus 1:7 underscores their responsibility to supervise the church’s spiritual life, including teaching ministries like Bible studies.
In the first-century church, teaching was centralized under apostolic and elder authority to combat false teaching (e.g., Galatians 1:8-9). House churches (Romans 16:5) were not independent but under the broader oversight of apostolic delegates or elders (Titus 1:5).
A Bible study group, especially one tied to church members, should submit to elder oversight to ensure alignment with sound doctrine. Hebrews 13:17 commands, “Obey your leaders and submit to them, for they are keeping watch over your souls.” Independence risks bypassing God-given authority.
I would think generally a church body inquiring after what is being taught to their church members by church members independent of the church itself is a definite concern for any of the elders God placed in authority over the flock.
I have no idea about any abuse, but I do know that when we submit to the authority God has placed over is what we are supposed to do as Christians, certainly we should be discerning and making sure we aren't following our flesh.
Just my opinion of course. I would note, that when we become members of a church we are usually agreeing not to teach against the stated beliefs of that church body openly.
For example, if I tell you I'm a Baptist, I'm telling you I quite likely wont be teaching against the doctrine of baptism by immersion, but if I tell you I'm a Particular Baptist I'm telling you it's likely far more than that I won't be arguing against today. If my face/name is associated with "that church on the corner", they have a right to know what you're saying.