For some background: the EU "Data Protection Directive" is a European Union directive which regulates the processing of personal data within the European Union, as explained in this Wikipedia article. Among these regulations is the rule that individuals have right for a copy of the data that has been collected about them.
About this the document A European Perspective on Data Protection and Access Rights says (on. p. 6):
Hence, although with a veiled expression, Art. 12 entitles the data subject to exercise the following four rights:
the right to confirmation as to whether or not data relating to the data subject are being processed by a particular controller and, if so, to obtain details of the processing (Art. 12 (a), first indent);
the right of access to one’s data, including the right to have a copy of the data in question with any available information as to their source (Art. 12 (a), second indent);
the right to have the data rectified, erased or blocked if they do not conform to the Directive, in particular if they are incomplete or inaccurate (Art. 12 (b));
the right to be informed about the logic used in case of automated decisions (Art. 12 (a), third indent).
Similar sentiments have been expressed in other documents, such as the "Charter of Fundamental Rights of The European Union", p.10:
Now many, if not all, religious organizations in United States keep registers about their members and to some degree also about non-members. For example the Church of Latter Day Saints (a.k.a. Mormons) have been known to baptize dead people (as explained here) and for that they presumably need to keep track of whom they already have baptized.
For example a comment from 2018 (before GDPR became enforceable) on this board here says that
From y experience as a missionary and later as a ward secretary the church is not at all compliant with GDPR, especially not the missionaries. Missionaries collect and store non-member data (contact details and teaching records) without any kind of written consent for an indefinite amount of time. Often, even when people ask for the records to be destroyed, this does not happen. Currently, teaching records are stored in electronic form and I believe are sent to servers in the US.
(Above is included simply because of being representative of the type of data that a religious organization may collect. The comment is old and may not reflect current practices at the LDS church.)
Mormons are not unique in the data collection either.
According to this article at Vice and this one at Washington Post, some churches also use facial recognition software to track attendance. The facial recognition software would be useless without an existing database of images against which to compare what it captures through the cameras.
On this note, does USA have a law either on the federal level or within any individual state, that gives an individual the right to all data kept about them by a religious organization?