This happened because the properties used the same flag variable. Switching
to RNA_def_property_enum_bitflag_sdna fixed this. However, I'm making
a patch for this because I don't properly understand the comments for
PROP_ENUM_FLAG and how they relate to the comment on enumbitflags.
The comment on the latter says "this only allows one of the flags to be set
at a time, clearing all others". To me that doesn't make sense if making
this "true" fixes the problem in this report.
Side note: I'd like to change the type of enumbitflags to bool,
it's only used that way.