In a comment I was told
Technically, [an Eruv] needs the permission of each non Jew that lives in the eruv if you are using his property or home, but practically we rely on the local government that has the right to search a home in a time of need, as enough authority to allow the eruv on their behalf.
What happens if someone in an Eruv, that is a non-Jew, wishes to explicitly be excluded from the Eruv? Is the consent from the government, following the logic above, superior to explicit rejection by the property owner?