The current document is directed to methods and systems that efficiently and accurately process log/event messages generated within distributed computer facilities. Various different types of initial processing steps may be applied to a stream of log/event messages received by a message-collector system and/or a message-ingestion-and-processing system, including masking sensitive fields to prevent exposure of confidential and sensitive information contained in log/event messages. Rule-based identification and masking of sensitive fields in log/event messages is currently provided by certain automated log/event-message systems, but current approaches suffer numerous deficiencies. The methods and systems to which the current document is directed automatically create sensitive-field dictionaries and associated logic and/or train machine-learning components to automatically identify and mask fields within log/event messages in order to address the deficiencies of traditional rule-based sensitive-field identification and masking.