Can conjoined twins be of the opposite gender of each other?
no, conjoined twins are always identical. Male and female twins are fraternal. You can only have identical twins that are conjoined because the conjoining happens in the early stages of pregnancy. Identical twins come from the same egg. Fraternal twins come from different eggs and can be either of the two sexes.
Conjoined twins ARE monozygotic and therefore normally of the same gender. There is an unusual condition where someone is genetically male, but the testes failed to develop and the person becomes (and feels and acts like) a woman in most respects except childbearing. If that happens to one twin only, you could get different genders.
