The libertarian party does NOT advocate for illegal immigration today. Only once NAP-violating governments are abolished, do they contend that the harmful effects of unconstrained immigration are non-existent. They argue that if you want complete freedom of movement, you must first give up all claim to nonconsensual government force, including taxation and redistribution of wealth. And even the most radical of libertarians include a "non-aggression" exception. They support screening to exclude violent criminals, security threats, and health risks. All of which are impossible if there is no monitoring or reasonable enforcement.
You know _damn well_ that in the context of actual politics in America as they stand TODAY, open immigration is a FAR LEFT position. It's undeniable to anyone arguing in good faith.