Is 'external' in 'external appearance' redundant when talking about a person's looks?

Solution 1:

The Free Dictionary by Farlex, has a section on quotes from classical literature and other sources using external appearance.

Charles Dickens:

Winkle, being engaged in the city as agent or town correspondent of his father, exchanged his old costume for the ordinary dress of Englishmen, and presented all the external appearance of a civilised Christian ever afterwards.

Wilkie Collins:

Vanstone's youngest daughter ran up to him at headlong speed, with every external appearance of having suddenly taken leave of her senses.

Dickens again:

Maylie was every [sic] ready and collected: performing all the duties which had devolved upon her, steadily, and, to all external appearances, even cheerfully.

And so on. Go to the link for many other examples. These examples, and many of the others, use external appearance as a flag: there is something beneath the surface -- a difference between the exterior and the interior.

Solution 2:

There are different nuances.

If talking about a person's looks then "appearance" should be used alone.

However in the phrase "should we judge people by their external appearance?" it is not just physical appearance (looks) but also the way they behave outwardly that is meant by "external appearance". The alternative to judging by external appearance is not judging by the state of their internal organs. Rather it is to judge by the internal motivation or personality.

She is a bit rude, and sometimes says very unkind things to people, but actually she has a heart of gold and doesn't mean to upset anyone. If you ever need a friend you can always rely on her.

That is the sort of contrast meant. Of course her heart is not really made of the precious metal.

It could be the other way round.

He is a very polite old gentleman, but it would be a mistake to judge by his outward appearance. In reality he is a devious and scheming person, just waiting for the chance to defraud you.