Do cojoined twins always have the same sexual preferences or have there been instances where one was gay and the other straight?
You do realize, of course, that conjoined twins are extremely rare, and that for most of the portion of history when they could have survived past infancy, sexual preference wouldn’t be common knowledge? I doubt that there currently exist any sexually mature pairs of conjoined twins.
For identical twins in general, though, the question might have some merit.
Richard Pillard of the Boston University School of Medicine and Michael Bailey of Northwestern University published a study in 1991, “A Genetic Study of Male Sexual Orientation.”
Among twin pairs where one twin was gay, Bailey and Pillard found that:
52 percent of the identical twins were both gay
22 percent of the fraternal twins were both gay
9 percent of the non-twin brothers were both gay
11 percent of the adopted, or genetically unrelated brothers were both gay.
Chronos, in fact there exists at least one set of sexually-mature conjoined twins.
For the life of me I can’t remember their names, but they are women joined at the skull. One of them is making a name for herself as a country singer.
I recall seeing a TV interview where they were asked how they dealt with a situation where the other twin was being sexual with someone. They basically responded to the effect of they “switch off” for the duration.
I know this was kinda a highjack… but an interesting fact nonetheless.
Max 
More than one such set exist.
A couple years ago one of those daytime shows had a good half-dozen conjoined twins on, and all of them were sexually mature. Since then, one pair has passed away but presumably the other five are still around.
At one point the audience ask the sex question of two brothers, and both said “none of your business - that’s private”. Good for them.
Maxxxie, you’re thinking of Lori and Reba Schappell. They live in Pennsylvania.
Those women joined at the skull are awesome! I’d like to hear an account of one of her sexual encounters from the man . . . he must be quite a character . . .