Your idea of a free and open border will drain resources. It will also create a huge backlog when trying to grant all of those poeple citizenship, the government would have to hire MORE poeple and buy MORE electronics to get the job done, causeing more spending and thus draining resources.
Your barbecue metaphore also only works if they are actually invited. LEGAL immigration is just fine, but illigal imigration is not.
Protip: you make a much more compelling argument when you take the time to speel properly.