Select all faces with same HEX value in edit mode

Here you go:

import bpy
import bmesh
from mathutils import Matrix, Vector

yuv = Matrix(((0.299, 0.587, 0.114),
        (-0.14713, -0.28886, 0.436),
        (0.615, -0.51499, -0.10001)))

class MESH_OT_select_similar_color(bpy.types.Operator):
    """Select faces based on diffuse color similarity"""
    bl_idname = "mesh.select_similar_color"
    bl_label = "Select Similar Color"
    bl_options = {'REGISTER', 'UNDO'}

    threshold = bpy.props.FloatProperty(name="Threshold", description="Use 0.0 to select faces with equal color only, larger values to select more dissimilarly colored faces too.", min=0.0, max=1.3271, subtype='FACTOR')
    extend = bpy.props.BoolProperty(name="Extend", description="Extend the selection")

    @classmethod
    def poll(cls, context):
        return (context.object is not None and
                context.object.type == 'MESH' and
                context.object.data.is_editmode)

    def execute(self, context):
        context.tool_settings.mesh_select_mode = (False, False, True)
        ob = context.object
        me = ob.data
        bm = bmesh.from_edit_mesh(me)
        
        mat_active = ob.active_material_index
        mat_diffuse = {i: yuv * Vector(mat.diffuse_color) for i, mat in enumerate(me.materials)}
        
        for face in bm.faces:
            sel = (mat_diffuse[mat_active] - mat_diffuse[face.material_index]).length <= self.threshold
            if not self.extend or (self.extend and sel):
                face.select_set(sel)
        bmesh.update_edit_mesh(me)

        return {'FINISHED'}

def draw_func(self, context):
    self.layout.operator(MESH_OT_select_similar_color.bl_idname, icon='COLOR')

def register():
    bpy.utils.register_class(MESH_OT_select_similar_color)
    bpy.types.MATERIAL_MT_specials.append(draw_func)


def unregister():
    bpy.utils.unregister_class(MESH_OT_select_similar_color)
    bpy.types.MATERIAL_MT_specials.remove(draw_func)


if __name__ == "__main__":
    register()


It selects based on similarity (not sure how well it works for more complex cases). It adds an entry to the material specials menu. Threshold slider and extend option in the redo panel (3d view).