Rundown can be defined as being old , dilapidated,and worn out. So, when you say a rundown Church, it is probably a church building not used for services. Maybe an abandoned building.
A redundant church, now referred to as a "closed church", is a church building that is no longer used for Christian worship. Link
As we believers usually say, that a church is not the building but the people that are members are the church. But I guess in this case, it is emphatic that it is the building bring talked about here.
So, a redundant church is not all that a big deal these days though because it can be renovated or better still sold out for a good price.
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