GDPR does not distinguish between public or private data.
GDPR handles public data through propagation. If you download public data that is GDPR covered, the data you downloaded also becomes GDPR covered. You are required to follow all GDPR regulations while handling the downloaded data.
Remember, GDPR covers almost all "collected personal data". It does not matter if the data was originally public, and how/where the data was collected. It's all covered.