In the wake of the recent vote in Ireland, there is some concern about what the Church's teachings can say to the new generation. To understand what can be said, first you must understand what the new generation is endorsing. It is not (merely) a different position on a few discrete issues. There's a developed and unified mode of thought at work behind it. It tracks to John S. Mill, but has filled out over time.
The first assumption of this new philosophy is Mill's assumption, which is that the important element in human life is the individual. Where Aristotle thought (correctly, I believe) that societies are formed by families, Mill took the Modern position that the thing that comes before society is a state of nature made up of radical individuals. This assumption is unquestioned in the new philosophy as far as I can tell. The individual and the individual's will is the thing that matters.
The second assumption follows from the first: the individuals we are talking about are fully-formed adults. The first assumption means that the wishes of an individual will always be selected for when they come into conflict with the interests of families considered as a whole. The second means that the wishes of adults will be placed before the wishes of non-adults: abortion is at the will of the adult individual who is pregnant, without other considerations. The family structure that is best for children is the one that is best for the adult individual parent given custody of them, so long as that structure does not produce adults who are out of line with the new philosophy. Homeschooling is a questionable practice; single motherhood is not.
Those are assumptions, as I said: they are not argued for, but taken as given.
Proceeding, then, given those assumptions, the philosophy is that sexuality should be regulated this way:
1) Adult individuals should be free to choose.
2) Freedom to choose is not compatible with any sort of coercion.
3) Therefore, sex is fine as long as it is consented to freely, verbally, and enthusiastically.
It's a very simple philosophy, but it is coherent. Many on the right make the mistake of assuming there is some conflict between the left's position that women are the equals of men in all respects, and that they need special protections in college, in the office, in the workplace in general, from harsh language or offensive terms. All of it follows from what has been said above. Both the man and the woman are equals in that they are free to choose. However, men are physically bigger and stronger; in addition, it is argued, society provides men with unearned power over women in various ways. Thus, to ensure that sex is always only fully consensual, we must regulate all sexual interactions to ensure that there was no power relationship providing any sort of coercion. We should ensure that there was clear, explicit, verbal consent and that such consent was really desired in a deep way.
The reason you get 'gay marriage' out of this is that there's absolutely nothing in this philosophy to speak against it. It's fully consensual, and an association of adults, so it's perfectly fine. There's not only no reason to be opposed to it here, there's no room for a reason. The principles are clear bright lines, and they admit of no exceptions.
From this, then, you will not get bestiality and pedophilia in spite of right-leaning arguments to the contrary. Kant thought you would, so it's not a foolish position, but it depends on assuming that the bright lines of the old system are the only possible ones. There the bright line was human nature, and it is obvious that sex fills a natural and necessary function. You can draw a bright line between those acts that do and those that do not fill natural functions. That was the old position, and it is a rational one. The new argument rejects the concept of human nature, however, in favor of individual will. There is just no room in the system for a concept of nature that should constrain will.
You will not get bestiality because consent is not possible. There is no slippery slope there. You will not get pedophilia because of consent issues, and the underlying assumption that this is a system for adults. The slippery slope there is limited to arguments about just how young you have to be before you can't clearly consent, but there's no danger of that line falling beyond a certain point.
What you will get is polyamory and plural marriage, and all of the trans-* desiderata. Those things are perfectly in line with this philosophy, and there is no reason to oppose them possible within the system.
Now, the reason to spell all this out is to address the question: what can the Church say to people who believe this philosophy? Well, you can't persuade them to adopt the old standards without first persuading them to abandon this entire mode of thinking about sexuality (which they will call "my sexuality," because everything is fully individualized in this philosophical structure). You have to show that the whole mode of thought is to be rejected, and then begin again showing why the traditional mode is a rational and proper substitute.
What you need not do, and ought not do, is argue for the rules. The rules follow from the structure. What you have to do is argue against their structure, and in favor of the traditional structure of reasoning from things we can observe about human nature.
How do you argue against the structure of the new philosophy? There are two general modes of argument that can be effective.
1) Argue against the assumptions. It happens that the assumptions are both badly wrong, so a lot of headway can be made here. Point out that these assumptions exist, and that the structure depends on both of them being true. Show that they are false. Human beings do not come into the world as radical individuals. We come into the world dependent on those who brought us into the world, and who care for us until we are able to take care of ourselves. That is to say, we come into the world not as clean actors free to choose anything that they want so long as it does not harm others, but as members of a pre-existing society who carry debts and obligations to those who helped them when they were weak. Those debts point forward to the next generation. We are duty bound to think about what is best for them, and not only about ourselves.
2) Argue against the good being pursued. The good is pleasure. Mill's philosophy believes that life is properly structured around pursuing pleasure and avoiding pain, according to rules (such as the three rules of the new philosophy) that make sure that these opportunities are as widely available as possible. But pleasure is a terrible standard for ethics. It is opportunity for pleasure and pain that ethics needs to control, because it is in temptation of pleasure or danger of pain that we are most likely to do wrong against others. Ethics needs to focus on how to ensure that we don't give in to our temptations to pleasure as much as it needs to talk about how we stand true to our duty in spite of the occasion of pain. Mill's rules are inadequate because they leave in place the idea that we should chase pleasure and flee pain as much as possible without being unfair to others. What we should be chasing and fleeing is something else entirely.
We might begin by saying that we should chase what is honorable and flee dishonor. (Aquinas says that, in his treatment of the virtue of magnanimity). Honor and dishonor are not personal like pleasure or pain, but have to do with relationships between human beings. They are the first answer to the idea of radical individualism as the proper seat of the good. The honorable is always about what you do from duty, and the dishonorable is always about letting others down who had a right to depend upon you.
Of course the Church will not wish to stop with honor and dishonor. It has something more to say, something that can become clearer to those who have begun following you on this road. When you have begun them in this direction, so that they see that their lives have some better end than pleasure, you will be doing again your ancient service to humankind.