Is saying "but nevertheless..." redundant?

Solution 1:

It isn’t redundant, not least because but is a conjunction and nevertheless is an adverb. The OED has around 40 citations for but nevertheless, including this, for example, from the poet Stephen Spender:

Leaves of Grass is a vague, formless, but nevertheless impressive and rhapsodic Aeneid of the American Civil War.

But signals a contrast, while nevertheless tells us that what is to come is said in spite of Whitman’s work being vague and formless. But on its own would not have achieved this effect. The OED editors themselves use the two words in the same way one of their definitions:

something unusual but nevertheless taken as part of one's ordinary duty or routine.

Solution 2:

I think the purpose is that it gives the sentence a different flow than nevertheless alone.

Nevertheless is a different kind of opposition than generic but - it emphasizes independence, "not being affected". So, the choice between but and nevertheless gives a somewhat different impression, conveys a different message.

Meanwhile, nevertheless is a word to usually appear at the beginning of a sentence. Normally, you'll see:

There is clause A. Nevertheless, clause B is true.

This is not entirely the same as

There is clause A, but clause B is true.

Now if you want to retain the first meaning, while obtaining the uninterrupted flow of the second example, you'll use both:

There is clause A, but nevertheless clause B is true.