Obviously, given the context, I am not trying to say immigrants don't pay taxes or follow the law. I am saying the the job of a government is to look after its own. If you have some better term for "its own people" go for it.

I'd also say, immigrants are only temporary non-citizens. If they are immigrating to stay, then it's the government's job to take care of them. Countries like the US and Australia were founded on immigrants.

If their loyalty is not to the country they are immigrating to, and is to their previous country's government, I am not sure why it would be a priority to support them.

I'm not being sarcastic this time. You seem to have missed the zeitgeist, especially among younger generations. For them, it's very much true that the government shouldn't look out for the interests of its citizens over the interests of people in general, and they do think it's racist if the government does this. It's impossible to explain to them the very simple game theory implications of such policy, and it's difficult to argue that the government isn't already doing it (in the United States, in other countries it's impossible to argue that).

>If their loyalty is not to the country they are immigrating to

This goes against human nature. Loyalty would come later, not before or even immediately.