In the movie Logan, why do the mutant children need to cross the border into Canada? What makes sure they won't be hunted by Transigen/the Reavers there?
Why do the need to reach Canada?
Gabriela and Laura explain this in the movie. They believe a sanctuary called "Eden" exists, and that if they can reach the coordinates in North Dakota, that they will be granted passage to it.
Logan is skeptical, seeing as that Eden and the coordinates seem to come from an old issue of an X-Men comic. Still, upon arrival at the coordinates, we learn that there is some sort of sanctuary across the border, and that the refugee mutants will be granted access.
Why do they believe they will be safe?
Because that's the rumor and story they've been told. A large theme of the movie is hope for the future and faith. Laura is largely taking it on faith that Eden is even real, never mind that they will be safe from persecution there.
Will/would they actually be safe?
Since we never learn the true nature of Eden, or what defenses they have, we'll never really know for sure. However, Transigen and the Reavers clearly do not worry about legalities or borders, as they crossed the US-Mexico border in pursuit of Laura. It's unlikely that they'd care much about the US-Canada border either. If any Transigen or Reaver forces remain post-Logan, they would likely still pursue the refugees into Canada and Eden.
The movie does not answer this directly, only by implication. In real life, a country would not permit a paramilitary force like Transgen to operate with impunity within its borders. It appears from the movie that Transigen can do just this. This is most likely because the future governments have some combination of being:
A. In league with Transigen
B. Corrupted by Transigen, bribed to turn a blind eye to their illegal activities
C. So consumed with hatred of mutants that they turn a blind eye to their illegal activities
D. Unable to stop Transigen because this is the type of dystopian future where the country is ruled by megacorporations like Transigen, with the government mostly a figurehead.
E. Unable to stop Transigen because they are weak and ineffective at maintaining law and order.
We can infer from the movie that one or more of these is true of the US and Mexico, but there is no particular reason to believe this is also true of Canada, and the implication is that it is not true - that Canada is still able to maintain law and order within its borders, and would attempt to meet any invasion by Transigen with police, military, and/or cyborg superhero forces. While the Reavers presumably could pursue the mutants into Canadian territory, they may choose not to because they fear being captured or killed, or perhaps Transigen has ordered them not to because it is likely to fail and they don't wish to lose their operatives and/or face sanctions from the Canadian government.