Neither has a lock preventing them from being exported.
Is there a sort of “count” of exported event types in the Gramps Gedcom Export? Why aren’t they both there?
Gramps treats birth and death events specially. To allow the reports to select a single event date/place, the first event of this type is used as the primary event. For better or worse, the GEDCOM export also only exports a single birth or death event, even when several are present.