Learn English – Word or idiom for someone holding (seemingly) contradictory views

Does "cringe-making" help? I think you're trying to express a feeling of discomfort created in the viewer, irrespective of the other person's self-awareness. I saw this word used to describe moments in Vince Vaughan's performance in the movie "The Dilemma."

self-righteous

confident of one's own righteousness, esp. when smugly moralistic and intolerant of the opinions and behavior of others.

Also from Wikipedia:

Self-righteousness (also called sanctimoniousness, sententiousness, and holier-than-thou attitudes) is a feeling or display of (usually smug) moral superiority derived from a sense that one's beliefs, actions, or affiliations are of greater virtue than those of the average person.

Self-righteous individuals are often intolerant of the opinions and behaviors of others.

Also pharisaical fits to your example:

Someone who is pharisaical preaches one thing and then does another — not a good trait for politicians or even playground pals.

Why use pharisaical when you could say hypocritical? In general, you would probably use the word in especially severe cases of hypocrisy, particularly when someone is not only a hypocrite, but acts superior and is being particularly annoying about it.