I don't think the comparison is apt.
The United States is not a house owned by just a single person or family.
It's a vast democratic nation with loads of space, inhabited mostly by people whose ancestors haven't even been on the continent, much less in the country, for more than a few generations.

The use of inapt metaphors are used to hype up nationalistic fury that is then often turned against other people - such as non-Christians. Christian Nationalists believe, after all that the USA is a Christian nation. The border hyperbole is part of the Christian Nationalist obsession with drawing borders around a nation for Jesus.

So, instead of playing with inapt metaphors, let's be direct: Do you think that immigrants are mounting an invasion?

@CliffordCook It is not managed well atm, I think this is undeniable. So numbers entering are unknown and uncontrolled.
First, can we agree these economic migrants are uninvited?
This is the best analogy I can think of, but in no way am I referring to those entering the states as less than human; insects. They are people who wish to migrate and I do not blame them. If there is a problem, it is the host countries management of it's international land border causing it.
Ant's like to come into houses, cockroaches, spiders etc. But when numbers become overwhelming, it is not a misuse of language to call that an invasion. Yes, the US is not a house, neither is the Earth but we refer to that as our home.
I totally agree "invasion" is inflammatory language but it is not incorrect language wise from a technical use of language angle. Invasion does not necessarily mean the invaders have ill intent either, just means uninvited and so unprepared to absorb them, instead you react. Unmanageable numbers are crossing the US border from all accounts. And it seems to me, it is affecting citizenry. So management seems broken so needs fixing. But you cannot fix a problem if it is denied there is a problem.
To this foreigner's knowledge the USA is not a Christion Nation, it is secular. All have the freedom to worship who they want over there as far as I know. Same Australia.

@puff The United States is not a Christian nation. The problem here is that Christian Nationalists are attempting to convert the USA into a Christian nation, and they're using the language of invasion to promote their ideology.

How did I know that was a PUFF response before I read who posted it?