Just because some people who say "no one is illegal" also say "no more borders," that does not automatically mean that the former implies the latter. If that were the case, we could paint everyone who agrees with Nick Fuentes on any point (including, in the extreme, "nice weather we're having today") as a antisemite. The old joke linking dietary choices to Nazism ("You know who else was a vegetarian? Hitler!") is meant to make light of this logical fallacy.

The grandparent post accurately captured what I have understood people to mean by "no one is illegal" -- it is meant to protest a dehumanizing way to describe a class of people.