Their value system does not consider consistency as a virtue. This is why shaming them as hypocrites does not bother them or resonate with their supporters.

To have an affect, the shaming needs to reflect their values. For example, being lazy and not wanting to work.

Sarah is too lazy to do good work that would hold up to public scrutiny, so she's trying to change the law so she can hide her low quality work.

This has a better chance of getting her supporters to question her actions, putting her on defense.

Shaming based on civilized values does not work on the uncivilized.