In Salesforce, you can grant read access to Custom metadata types and custom settings via profiles and/or permission sets.
You can read Salesforce's instructions on how to do this for Custom metadata types in Control Read Access to Custom Metadata Types.
And for custom settings check Grant Permissions on Custom Settings.
Example for a Profile:
The same principle follows for Permission Sets:
How to retrieve Custom metadata via 'Compare and deploy'
To retrieve Custom metadata types access, or custom setting definitions access for a profile, you need to include Profile and Custom object in your metadata filter before the comparison.
To retrieve custom metadata types access or custom setting definitions access for a permission set, you need to include Permission set in your metadata filter.
You could use Gearset's Default comparison filter for either of the above, as this pre-defined filter includes all these metadata types.
Where to find this metadata in the comparison results
You will find both the custom metadata type access and the custom setting access in the comparison results as part of the Profile or Permission set itself, rather than being separate line items.
They will be listed as <customMetadataTypeAccesses> and <customSettingAccesses> in the XML in the diff viewer in the bottom half of the screen.
In our Profile example:
In our Permission set example:
Note: The Profile or Permission set may appear twice in your Gearset comparison results, so make sure you find/select the one that has this access included.