So Jesus appoints leaders (undershepherds) to his local fellowships of believers. The Holy Spirit is involved in all these points.
The Holy Spirit is given by Jesus to his people
The Holy Spirit binds Jesus people to him in union
The Holy Spirit binds the people of the fellowship to one another
The Holy Spirit connects members of the fellowship to their leaders
That last one is what seems to be said in Acts 20 when Paul speaks to the Ephesian elders.
Acts 20:28 “Keep watch over yourselves and all the flock of which the Holy Spirit has made you overseers.”
Who are the elders responsible for? The Holy Spirit knows who. The Holy Spirit determined who the elders would answer for.
What does this have to do with dual church membership?
It means that the Holy Spirit has given you have one set of pastors/elders. Think about that. Someone will answer for you. Someone will face more stricter judgement (Jam 3:1) on your behalf.
If you go to two churches, what are you doing to your leaders? Are you making two groups of elders responsible for you at the same time? Are you causing one group of elders to feel the weight of responsibility and prayer for you – when they really don’t need to?