The people complaining about the border crossing thing are logically equivalent to the people getting killed for somebody else's children, rather than the people doing the killing for their children.
So that tweet is not a like to like comparison and it IS logical that some people both and at the same time would kill for their children AND dislike people crossing borders for theirs - not the same side of the action and not the same kids.
The beliefs of the anti-immigrant crowd are Logical if they genuinelly believe that the downsides of immigration for themselves outweigh the upsides. Where these beliefs are open to dispute is in the truthfulness of the "information" which they used to reach the conclusion that immigration is bad for them and in the Ethical and Moral aspect of how they think immigrants should be treated.
PS: And I just want to add that it's a personal peeve how the whole Immigration subject has been reduced (probably by slimy Politicians and Think Tanks) to one-dimensionality by both sides of the Identity Politics theatre in broken "Democracies" and then parroted by unthinking simpletons, when even putting the whole "should there be nations and borders or not" aside, I can think of at least 3 different Moral principles that should inform one's views on the subject of people from some other country coming to live in one's country: The Duty to Help those suffering (which yields the concept of Refugee), the Duty of a Host to invited Guests (which applies to the treatment of Legal Immigrants) and what is acceptable to do to uninvited outsiders (which applies to Illegal Immigrants who came to improve their personal upsides, not because of "suffering") all of which yield way more moral conundruns than the one-dimensional take (for example, how bad one's lot in life needs to be to trigger the Duty Of Help of others), introduces the question of were are the limits of one's capability to help (the Duty Of Help takes in account on how far one is capable of helping) and even introduces an additional Active element (should we activelly seek the worst off to help them?)
Without the slimy fake left (or just plain incompetent) politicians doing their loud performative "moralism" on top of the Think Tank created hyper-simplification of the subject of Immigration, the Far-Right would have way more trouble engaging people with their simpleton anti-immigration slogans, because for example only the worst of the worst kind of people would deny the Duty Of Help or the Duty of a Host to invited Guests - this shit should be discussed in the context of a Moral framework, not dealt with with sloganeering.