wbparsevalue accepts multiple strings to parse in one request. These are passed as a pipe-separated list via the values parameter. This means that any client code, including the Wikibase UI code, needs to use the alternative separator character:
The API offers an alternative separator for multivalue parameters: If a string starts with ASCII code \x1F (Unit Separator), any other occurrence of \x1F in the string will be treated as a separator, and pipe characters are treated as literal. See ApiBase::explodeMultiValue() for reference.
Clients that want to allow pipe characters to be present in aliases need to prepend the parameter value with \x1F.