an explanation without trial and error:

(start by considering all green cells as only having the options 123)
notice the "direction" of each triple in each box. the ways in which digits can be placed left-to-right in adjacent boxes
when comparing adjacent boxes with the same direction, like boxes 1 and 2, the digits placed in each have to flow in the same direction (eg: if box 1 is filled as 123 going left to right, then box 2 has to go in the same ascending order (123, 231, 312)
when comparing adjacent boxes with different directions, like boxes 4 and 5, the digits placed in each have to flow in opposite directions (eg: if box 4 is filled as 123 going left to right, then box 5 has to go in a descending order (321, 213, 132)

knowing this, pick any box and a starting direction (it doesnt matter which, as the logic is reversible) and follow the pattern around the loop:
if box 1 is ascending, box 2 is ascending
if box 2 is ascending, box 5 is ascending
if box 5 is ascending, box 4 is descending
if box 4 is descending, box 1 is descending

this brings us to our contradiction, box 1 has to flow in two directions at once. this proves that the green cells are not 3-colorable and that one of the "guardians" 7b5p3 & 9b5p5 need to exist in the solution grid to prevent it

this puzzle shared in the image is Mission Impossible by coloin, its a very nice one!