The Events Calendar itself doesn’t have any functionality that would solicit and record personal information from visitors to your site automatically, with the possible exception of our Event Aggregator import service (which can pull in event data from external sources such as Facebook, however this is a paid service that is not enabled by default).
However, it would certainly be possible for you/your team to add personal information in various places (a good example might be the personal details of any organizers you add to the calendar). At this time, there are no tools to help find and redact or remove information of that nature from within the plugin, though I’d expect in most cases it could be done manually without too much effort and – ultimately – this isn’t much different from a scenario where you or your team add personal details to regular posts or pages.
I hope that helps!
