How to set AnypointMQ with circuit breaker and force that no more messages are processed once the circuit is open in Mule 4.x

To achieve this use case you need to ensure that messages get processed one by one and also to tweak the prefetch. Setting the max concurrency of the flow to 1 and the prefetch to 1 should suffice for this behavior.

The connector configuration will look like:

<anypoint-mq:config name="Anypoint_MQ_Config" doc:name="Anypoint MQ Config">
		<anypoint-mq:connection clientId="${ID}" clientSecret="${Secret}" />
	</anypoint-mq:config>

The Flow with max concurrency = 1:

<flow name="test-circuitBreakerFlow" maxConcurrency="1">

The AnypointMQ message subscriber:

anypoint-mq:subscriber doc:name="Subscriber" config-ref="Anypoint_MQ_Config" destination="${yourQueue}" acknowledgementMode="MANUAL">
			<anypoint-mq:subscriber-type >
				<anypoint-mq:prefetch maxLocalMessages="1" />
			</anypoint-mq:subscriber-type>
			<anypoint-mq:circuit-breaker tripTimeout="${time}" onErrorTypes="${type}" errorsThreshold="${threshold}" tripTimeoutUnit="MINUTES"/>
		</anypoint-mq:subscriber>

Please also refer to the Mule Application example attached showing how the behavior described in the article works.

Disclaimer: This solution provides a suggestion that should be considered in conjunction with your specific use-case and requirements and does not represent a complete solution for all circumstances.