Current thinking is that sexuality isn't determined by genetics per se, but by epigenetic and developmental factors such as the hormonal balance in the womb during brain development. So it would be possible for alternate-timeline copies of the same person to have different sexualities, as we've seen in the Arrowverse with Captain Cold vs. Citizen Cold (and with John Trujillo and Black Condor in Freedom Fighters: The Ray, though that series doesn't really fit into Arrowverse canon). Although of course we have also seen instances where doppelgangers had the same sexuality; e.g. Earth-1 and Earth-X Sara Lance are/were both bisexual.
See also Orphan Black, where the various "genetic identicals" (clones) of Project Leda covered the gamut of sexualities from hetero to bi to lesbian to trans male.