I agree with you completely about the Golden Rule. It will be a wondrous day if humanity would do things in this light. Until then, we are dependent on laws and measures to ensure that we are going there.
I would say that all well-off countries have the obligation to open their gates to those who are struggling for survival. However, every country has the right to defend the way of life it has made its own. I would make any immigrant sign a document that he is being accepted on the condition that he respects the constitution, the laws, and the character of the country - otherwise he will face the consequences. Maybe this is too much for the liberal left - but I consider myself a liberal and would support such a measurement. Enforcing this is difficult, but is the only way to strike a fair balance, imo.