I've never seen anything about race in the parish records. Nationality (German, Finn, etc.) is mentioned. Religion (Jewish, Catholic, Baptist, etc.) is mentioned.
Records were kept in the parish and once the parish is known, people of any nationality, religion, or race would be in those same records.
Your ancestor could be found if you provide enough details to identify a parish. If he was from Africa, for example, or if an ancestor was from Africa, that could be determined if the records went back far enough.
Maybe there is a record showing race in another type of record. Swedes should know.