How does this sound as an endorsement of skepticism as an approach to life that says all our opinions should?

An opinion is only as valuable as its practical application. Therefore, an opinion should be revised whenever circumstance requires the opinion's revision. There's no one rule of thumb that can be applied to every situation.

Adolf Hitler had a prejudice. There was an abyss below.

Truth be told, "prejudice" does not exist. "Prejudice" is "pre judgment", making a choice prior to examination of the facts. But, all prejudice is based on examination of the things accepted, by the one choosing, as "facts". A cop is prejudiced to believe that the guy pointing a gun at him will pull the trigger, and the survivor will be the one of them that does not hesitate to do so. This is an examination of facts, and a consideration of probability. The guy with the bad aim may need a lot of tries, but the guy with the good aim will die if he never chooses to pull the trigger. It is not a question of who is the best shot. It is a question of who is most prejudiced.

Prejudice is not a bad thing, in and of itself. The source of the judgment may be bad. To decide based on irrelevant information is bad. Yet, the cop who shoots a guy with a squirt gun in his hand may be found guilty.

Is there an abyss? Absolutely.

But, to suggest that prejudice is a source of error is errant.

Not everything is in doubt. Many things are, perhaps most of them, but many are certain. Adolf Hitler, Jeffrey Dahmer, they are real, and they were evil. Gravity exists, and can be quantified, and any perception of it is without prejudice. One plus one equals two, always and in every case.

"We can't know anything?" Wrong!

"We can't know everything"! Absolutely!