Children of identical twin sisters and brothers have indistinguishable DNA similar to full siblings.
Fraternal twins do not have extremely similar DNA because they are conceived due to fertilization of two separate eggs of the same mother at the same time. Fraternal twins run in families, making it a hereditary probability passed on by such mothers.
If two sets of parents are fraternal twins, their offspring share about 50% of their DNA; the double cousins will share about 25% of their DNA.
However, identical twins’ DNAs barely vary, with only tiny details like a beauty mark separating them. They inherit the same DNA from their parents. If twin sisters reproduce with twin brothers, the resulting children are genetically indistinguishable from full siblings. Legally, they would still be first cousins.