Every time the number of open or active microphones in your church system increases, the system gain (or volume) also increases.
The effect of this is greater potential for feedback as more microphones are added, just as if the master volume control were being turned up.
In addition, unwanted background noise increases with the number of open microphones. Here, the effect is a loss of intelligibility as the background noise level rises closer to the level of the desired sound.
A good solution is to activate microphones only when they are addressed and to keep them attenuated (turned down) when not being addressed.
In addition, when more than one microphone is addressed at a time, the system volume must be reduced appropriately to prevent feedback and insure minimum noise pickup.
An automatic microphone mixing system can be a lot of help in this situation. Essentially, it’s comprised of a special mixer and an associated group of microphones, and it’s function is twofold: to automatically activate microphones as needed and to automatically adjust the system volume in a corresponding manner.
In some automatic microphone systems, ordinary microphones are used and all of the control is provided by the mixer. In others, special microphones are integrated with the mixer to provide enhanced control.
There are several techniques used to accomplish channel activation or (gating) in an automatic microphone system.

A look at a basic automatic microphone mixer setup. (click to enlarge)
In most systems, a microphone is gated on when the sound that it picks up is louder than some “threshold” or reference level.
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When the sound level falls below the threshold, the microphone is gated off. This threshold may be fixed, adjustable, or even automatically adjustable.
In any case, the threshold should be set so that the microphone is not activated by background noise but will be activated by normal sound levels.
Traditional threshold systems distinguish between background noise and the desired sound only by level.
However, if background noise becomes sufficiently loud, it may activate microphones unless the threshold is adjusted to a higher level.
Subsequently, if the background noise decreases, normal sounds may fail to gate the microphones on unless the threshold is lowered as well. Threshold adjustment is critical to automatic mic systems of this type.
Some recent automatic mixers incorporate noise adaptive threshold circuitry. These have the ability to distinguish steady signals such as background noise from rapidly changing signals like speech.
They can automatically and continuously adjust individual channel thresholds as ambient noise conditions change.
I wanted to point out one technology not mentioned here: the gain-sharing algorithm. This is a way to provide auto mixing without gates at all - no thresholds to set (even automatically) and thus a more seamless mixing process. Most broadcast-quality auto mixers and larger scale applications now use this kind of system.