The essense of the ruling is that law doesn't apply to the clergy because this is a Christian nation. That's a pretty f'ed up ruling, even for the time.
That's the rationale for the conclusion - at its heart though, the ruling interpreted the statute to exclude clergy foreigners even though the plain text of the statute included them because they thought
that legislative intent trumped the actual text.That's why, if you read later on, Scalia hates it so much. No way in hell any judge (liberal or conservative) would interpret a statute that way today, and we're much better off for it.
Demonstrating the complete irrelevance of legislative intent in statutory interpretation is Scalia's great gift to the law (if not the greatest gift to the law of the latter half of the 20th century) - thanks for illustrating it to us...