Why should it care about the religion of man, then?
For that matter, why should it care about the invitation of man?
If there are rules a vampire must follow, and those rules can be satisfied through the agency of human beings, having been interpreted by human beings, then we have to consider what a human being means by invitation.
If a 4-year-old invites a vampire into his parents' house, does that count? It's not his house, either. If you think that a vampire can enter on the invitation of a 4-year-old then you must concede that people other than the owner can invite someone in. If you think that invitation is not valid, then you must concede that a vampire respects a hierarchy of rights.
I think that the state asserts a right to invite other people into your house which supersedes your right to prevent them. We call that overriding invitation a warrant.
What if the judge uses eminent domain to legally take ownership of the house when handing out the warrent? The state would become legal owner of the house, sends in the vampire police, and hand it back to the original owner later?
Or if the actual owner is the bank that the resident is in debt with. You fail to pay your debt and the bank invites repossessers and the police to evict you and take your stuff.
If I was a vampire, I'd definitely look for a job as a repossesser or a cop.