Asking for a friend

As always, it depends on the writer/DM

Assuming standard vampire mythology though, a warrant isn't an invitation to enter, it's permission for someone to enter against your will, with the backing of the government.

So, on a "magical" level, it wouldn't meet the criteria because the origin of that limitation isn't about a legal standing. It's about the space being lived in, and the construction of the space giving boundaries that can be/are present in a non physical way.

Foundations, doorways, windows, they all have a degree of "mystical" presence beyond their physical purpose, within this context but also in general. There's some beliefs out there about how a foundation has to be laid to make a space a proper limitation. It's akin to sanctified ground in a way.

And, depending on what stuff you dig into reading about this stuff, once that boundary is in place, the actual building/home could be destroyed, and the boundary can remain, a kind of ghost wall that can't be seen, but still has presence on a spiritual level.

With all of that in mind, the vampire would be unable to cross the threshold no matter what government agent said they could, unless that government could be said to be the owner. However, most of the mythology on this kind of stuff, ownership is irrelevant. What matters is who lives there, so even that might not work.

There's an Adventure Time episode wherein a vampire won't enter a "house" - not because they can't, but because they believe it would be impolite.
This is reminiscent of that.
- Ye and in Castlevania they explain that the sign of the cross works because vampires are an evolved predator species so putting a weird geometric shape in their face makes them confused and have a panic attack because they can't fathom it. So the cross works on hindu vampires too
- No self respecting vampire would do otherwise.
What if a house or the minimal requirements for the border was built overnight surrounding the vampire? Would they be able to leave? I assume it would be a distinction between whether it's the border or crossing of the border itself or if it's the whole house? Though invites could be rescinded and they get pushed out, right? So then it must be the whole house.
- OP is the correct answer. The reason vampires can't enter homes is because of the positive mental energy built up around the house as a threshold. Giving consent to a vampire to enter is allowing them a pocket through the threshold. Said threshold is built up through regular living. A family home with a stay at home mom and three kids will have a stronger threshold than an apartment lived in by a two-job worker. Some stronger vampires can break through weaker thresholds (depending on source). There are multiple supernatural beings that this threshold can (supposedly) stop, not just vampires. So just because someone else tells them they have legal permission to enter a home doesn't mean they'll be able. It's magic, not legality.
- Leaving shouldn't be a problem. It's the sanctity of "home" that prevents them from going in without the invitation. Those boundaries are meant to keep bad out, not in. That even applies to some of the rituals and prayers used to bless a home in general. They're usually phrased to bring good, and bar bad.
  Then there's also the fact that if you build around the vampire, you've made it part of the home, they no longer need an invite because they belong.
  Back in the older myths, there's no mentions of rescinding an invitation at all that I ever ran across. That's a very modern concept. I'm not certain where it started tbh, it's been years since I was deep diving vampire stuff, and I wasn't particularly paying attention to when things came around as much as the various myths existing. I was into it out of a combination of personal interest and gathering ideas for world building.
  I wanna say that the idea of a rescinded invitation expelling the vampire was brought into common thought in the movies, but I'm damned if I can remember for sure. Nor where it showed up first. My memory says it was somewhere in the eighties horror boom, but that might have been preceded by literary invention
  Now, if I was writing vampires that had to be invited in, I like the idea of the "magic" of home being powerful enough to physically expel them. But I tend to like to base my magical effects on something historic (No matter how loosely applied) when I can, and I'd likely use the basis of the foundation of the home being the seat of the magic. So I still wouldn't apply the effect to a foundation built around them. They'd be safe inside the boundary until they left.
  At most, I would have them feel uncomfortable there. Reason being for that much that the "life" of the home would be rejecting them. That's a concept I've played with a little as a DM/GM before.

Nope - the warrant gives them a legal right to be there, with or without your consent, but is absolutely not an invitation.

No, as a vampire still needs to be invited into the home. A judge can make the sun assaulting officers with death rays illegal but theres nothing they can change about nature.

I disagree. The most governments can straight up kick you out of your home, so it seems to me the cosmic laws of the universe that govern whether a vampire has been invited in would recognize the warrant as an invitation by the judge into the home.
- So in essence, all a Vampire would need is someone with the authority to let them into anyone's home. I wonder how one would define that authority?
  Ooh, what if the judge is the Vampire!
- Under this philosophy; citizens residing within states that have the castle doctrine would legally be protected from vampires while in their motor vehicles?
But couldn't the law be written so that a warrant once seen by the home owner must legally be considered a mandatory invitation, making the cop legally allowed to enter the home?
- A, this is why magic isn’t real
  B, the law can say whatever the fuck it wants it still can’t bend reality. More likely and much simpler, the vampire cop brings a non vampire friend who beats you until you “willingly” invite them both in and they plant drugs all throughout your house.
- just because they legally have to doesn't mean they physically have to though they could still not invite you in

They may be able to go in to perform police duties. Vampiric activities must be kept to a minimum.