re: Identical twins marry identical twins

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their dna will be as if they are siblings even though they are first cousins

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That's real hard to pull off. A bunch of gumps in Alabama just got really jealous!

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their dna will be as if they are siblings even though they are first cousins

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Actually, socially, they will be double first cousins. You are correct that - mutations aside - they will be genetically indistinguishable, other than as siblings.

First cousin simply means you and your first cousin share a set of grandparents. When a pair of siblings marries another pair of siblings (not uncommon in smaller communities), the resulting children share 2 sets of grandparents, making them double first cousins - double first cousins are actually closer in relation that true first cousins, but not quite as much as siblings - there is less genetic variation, but obviously have the same 4 donor grandparents.

But, with identical twins marrying identical twins - although not all that common (identical twins aren't very common to begin with), because essentially each twin is the clone of the other, there is even less - cousins through this arrangement have, genetically, the same parents.