Undertow is being used as a metaphor here.
In oceanic settings, an undertow is water flowing under the surface away from the coast. They're considered dangerous to beach goers as the person can get 'caught' in the undertow and pulled away from the coast. Swimming against the undertow often results in exhaustion and eventually drowning.
"the undertow of public disapproval" might be visualized as, not water, but public disapproval pushing them away from the safe 'coast' and into a dangerous situation.