A custom faction with the Binding trait will be unable to train spiders unless the race is Resoln.
The reason is because the spiders have this XML
<IsStartingUnitType>1</IsStartingUnitType>
and mirrored in the racetype of course
<StartingUnitType>Unit_BoundHarridan</StartingUnitType>
<StartingUnitType>Unit_BoundHoarder</StartingUnitType>
<StartingUnitType>Unit_BoundWidow</StartingUnitType>
However, there is absolutely no reason to have this <IsStartingUnitType>1</IsStartingUnitType> on them because they are already limited by access to the faction trait Binding (and some for techs). There is only a need for <IsStartingUnitType>1</IsStartingUnitType> when a unit has no prereqs and thus would otherwise appear for all races.
To make the spiders from Binding trait available for all factions simply remove <IsStartingUnitType>1</IsStartingUnitType> from their UnitType (and clean up the racetype while you're at it).
Also be advised that the Bound Hoarder requires the Black Quire technology which is limited to Empires. A kingdom that selects Binding will never be able to build those units (just as they will also not be getting special summons from death shards).