It should be, and in common nomenclature, it is.
But from my understanding of Constitutional law, it is not one in the federal sense.
That's why it is up to the States to stop this horde of multinational trespassers for exactly the reasons you mentioned.
States that have tried to stop the illegals have been told it is federal jurisdiction only. Securing the borders is a federal responsibility, though they choose not to do so.
Trust me it is indeed an invasion, whether it is legally one or not. If this current mass of illegals are refugees as the media seems to want to portray them; then the feds are not following laws for that either.
At this point our government is making up the law as they go along, as well as choosing to enforce or not to enforce as they choose. Legalities don’t seem to matter any more, if they did most of the current administration would be behind bars.