Final answer:
To successfully deploy custom setting data that references a profile Id to production, data templates should be used. This method accommodates environment-specific Ids during deployment.
Step-by-step explanation:
When deploying custom setting data that references the Id of a profile up to production, it is best to use data templates. These are deployment artifacts that allow for the referencing of organization-specific Ids, such as profile Ids, in a way that can be resolved in the target environment. A YAML file or an environmental variables approach could potentially be used, but those are more commonly associated with configuration settings, not direct deployment of data that includes Salesforce record Ids. A .gitignore file does not apply here as it is used for specifying untracked files that Git should ignore, not for deploying data. To successfully deploy, one should use a strategy that respects production Salesforce's unique profile Ids.