What strategies can be employed to secure sensitive data in log files?
I think the solution comes down to a broad spectrum of approaches that ensures data protection:


Data Classification: The most efficient technical strategy is to categorise the data at the point of creation rigorously. At its core, the developers are responsible for ensuring that all logged information is assigned a category.  Categorization can, for example, be achieved through Splunk Metadata which, in turn, can be used to direct log entries to different buckets based upon their data categorization.
Event Partitioning: There is often a desire to log sensitive information along side non-sensitive information. For example, if a new user was to sign up you may log:


Customer ID (Restricted)
Customer Type (Restricted)
Aquisition Source (Unrestricted)
Correlation ID (Unrestricted)


It is possible to split this one "Event" into two parts, one containing the Restricted information and one containing th Unrestricted information.  This aligns with the first point by allowing filtering rules to direct to different buckets.
Data Masking: In specific circumstances it may not be possible to categorise the data at source, in my experience logging solutions do allow for Masking Rules to X out sensitive data.  In the linked example a sed command is used to apply a regular expression to all data from a specific source.  Once the restricted data has been masked out then the event can be considered to be Unrestricted.  Care must be taken with the rule to ensure that information critical to an event such as a correlation ID doesn't match the Regular Expression used to match sensitive data.
Event Filtering: As a last resort it may be necessary to filter all events of a particular type or source into a separate bucket if they contain sensitive data that cannot be categorised or masked.  In this case the information in a restricted bucket could only be accessed through a Break-Glass mechanism to bypass access controls under the provisions of an incident.


With each of these solutions, testing is key to ensuring that nothing slips through the cracks.  Logging and Event Management must be considered to be a first class Non-functional Requirement with the same level of development rigour applied to a solution - including peer review and tests to ensure that data is properly categorised and partitioned in the tool of choice.