The Church can refuse to erase a baptism from its records. In the Catholic Church, baptism can only be received "once in a person's life" In 2014, the Court of Cassation rejected the appeal of a man who wanted to see the mention of his sacrament disappear from the parish register.
The decision of the Council of State is “interesting’ given the fact that it is the first time that it has to rule in the context of the application of the General Data Protection Regulation (GDPR)