In general, having a good data management plan will lead to FAIR data. In the case of privacy-sensitive data, it is possible to meet the criteria, but not to share the data openly. In this case you can make sure that a well-described dataset can be found online, while preventing the underlying data to be downloaded and used without permission.
If you anonymise your data, presuming the data is of limited sensitivity and you are very sure the data cannot lead back to the persons involved, you can share your data openly.
The FAIR Guiding Principles were put together and published in Scientific Data (Mark D. Wilkinson et al., ‘The FAIR Guiding Principles for Scientific Data Management and Stewardship,’ Scientific Data 3 (March 15, 2016): 160018.).
Not having FAIR research data is very expensive.
‘The cost of not having FAIR research data costs the European economy at least €10.2bn every year.’(Cost-benefit analysis for FAIR research data)