1. A processing unit for a data processing system including a shared memory system, the processing unit comprising: a processor core; and a cache memory coupled to the processor core, the cache memory including: a cache array; a directory; read-claim logic that services memory access requests of the processor core; and dispatch logic that, responsive to receiving a transactional memory access request issued by the processor core in response to execution of a memory access instruction in a memory transaction undergoing a current execution by the processor core, evaluates the transactional memory access request for dispatch to the read-claim logic for service by determining whether the memory transaction has a failing transaction state, and wherein the dispatch logic, responsive to determining the memory transaction has a failing transaction state, refrains from dispatching the memory access request for service by the read-claim logic during the current execution of the memory transaction and refrains from updating at least replacement order information in the directory in response to the transactional memory access request during the current execution of the memory transaction.