AVRO-1497, Schema.parse calls LogicalTypes.fromSchemaIgnoreInvalid on any schema that is expressed as a JSON object (anything except bare primitives).
That static method relies on a static cache based on WeakIdentityHashMap (WIHM).
WIHM clearly states that it isn't threadsafe ref
All of the Schema.Parser instances use that same static Schema.parse method.
The end result is that as-is it's only safe to have a single thread parsing schemas in a given JVM.