You are conflating not allowing them to be members of the church with not allowing them to attend. I am not a member of the SBC (I attend an Assembly of God church), but I think most true Christian churches WANT sinners to come to their churches - how else are they going to be saved if they don't hear the Gospel preached? We love them and want them to come to a saving knowledge of Christ. But that is very different from having them as members of the church while they are still sinners.
In churches like the SBC and AofG, Church members have the right to be involved in major decisions of the local church - whether or not to buy church property, hiring or firing a pastor, members of the board of deacons, etc. You don't want someone who is living an openly sinful lifestyle to be able to influence the operations of the church...
So attendees are sinners and members are not? Convenient.