If a set of male twins has kids with a set of female twins, would the kids be cousins or siblings?

First cousins.

If all the parents are identical twins, though, the kids would be genetic siblings.

Cousins...

Well, for starters males do NOT determine multiple births. Only the female determines that.

Human multiple births can occur either naturally (the woman ovulates multiple eggs or the fertilized egg splits into two) or as the result of infertility treatments such as IVF (several embryos are often transferred to compensate for lower quality) or fertility drugs (which can cause multiple eggs to mature in one ovulatory cycle).

They would be cousins.

HOWEVER - a DNA test MIGHT show their genetic relationship to be "sibling" IF the parents are IDENTICAL twins.

They will be cousins

The kids will be 1st cousins.

They'd be cousins. Family relationships don't necessarily reflect the amount of genetic similarity.

If both sets of twins were identical, the cousins would be genetically as related as siblings are. If both sets of twins were fraternal, they wouldn't be any more closely related than other cousins are. If one were fraternal and the other identical they genetic mix would be somewhere in the middle.

Cousins. It is not too uncommon for brothers to marry sisters. Twins, however, are a lot rarer.

Cousins. They don't all share the same parents.

cousins of course