We violate Scripture when we bring non-believers into our worship, that is for believers alone.
People are a little lazy, they would rather bring someone to church than tell the gospel to them, themselves.
A little embarrassed about the gospel, to the point that you would rather let others do it while taking the credit for their salvation because you brought them in? Just sayin!
God told every believer to speak the gospel to non-believers. There are no special classes of believers who are the only ones called to preach the gospel. We all have a responsibility to share it, by the power of the Holy Spirit we all have the fruit of Him Who lives in us.
We may have different roles based on our gender or age, but we have all been given the mandate to go into the world. The original language tells us that "the world" is where God has placed us.
Mark 6:15 ". 15 And He said to them, “Go into all the world and preach the gospel to every creature."
No where does God tell us to bring them into the gathering as non-believers. We preach to them in the world and when they become born again we bring them in as brothers and sisters in the Lord.