That’s why I said the analogy was imperfect. Because border guards (or the state) aren’t “inviting” anyone. It’s not an endorsement to let people in (unlike a friend to your house)
If I would push it further to the extreme, "you" are inviting yourself. You're not a guest yet, you're inviting yourself, showing up at a stranger's door asking to be let in.
Though I agree with you that analogies have limits.
I am not even sure of anything at this point, especially after reading the comments around, almost as if it was bigotry.
It could be a cultural / education difference too; I was taught that local cultures are equally legitimate as much as my personal culture.