Not in my experience - the insincere can be convinced to fall back to a different not-necessarily-sincere position, whereas the sincere tend to take an attack on their beliefs or actions as an attack on themselves.

The apposite consideration here is Dumas' razor, "I prefer rogues to imbeciles, because rogues sometimes rest."

(In the original French, "J'aime mieux les méchants que les imbéciles, parce qu'ils se reposent." Or various other renderings, e.g. "Je préfère le méchant à l'imbécile, parce que l'imbécile ne se repose jamais" ["... because the imbecile never rests"] or "Si je devais faire un choix, entre les méchants et les imbéciles, ce serait les méchants, parce qu'ils se reposent." It appears to be something Dumas fils said in response to Victor Hugo saying "Les méchants envient et haïssent; c'est leur manière d'admirer" ["The wicked envy and hate; it's their form of admiration"] and others liked and wrote down, not something he wrote, but it's a popular quote for a reason.)