It is available on the Public View of Red/Private profiles. If the profile has any data, it will be indicated in the yellow-border section (referenced but not visible). See the available information on this profile:
Varney-587
If there is no data referenced in the yellow-border section, then there is also no data in the data fields. So you already know if the profile does or doesn't have data that might match another profile's data. If you see no date in the Public View, then there is no underlying date for a comparison anyway.
For lower privacy levels, you can sometimes find the Open Profile request link by clicking the Family Tree & Tools tab and then the Contact link (or just scroll to the bottom).
Once you find the link for a given profile, save the link. You can change the WikiTree ID to fit the profile you want to request to be opened.
Just understand that not all requests will result in the profile's being opened. Some profiles may be deleted, as with Lindenhovius-6.