Officially why not? They would be next in succession and wouldn't need to produce an heir. I don't think that any kind of surrogacy or adoption would be looked on favourably so they would have to resign themselves to being childless.
Unofficially? well I suspect it would cause much upset and high blood pressure in court circles! Also unofficially, i can't see a same gender consort being allowed!!
I think the difference today is not just that being gay is now legally and socially acceptable, its how much harder it is to keep such things quiet. I have said on here before, that in London, the Wallis Simpson affair was common gossip but the papers had agreed not to publish anything. Now we have the internet, phones with cameras in, long range lenses and teeny microphones. If such a thing happened, barring an accident in a Paris tunnel, its going to be known about.