I think it's important to note that having young Jennifer meet her older self isn't said to definitely create a universe ending paradox, but that it could create a universe ending paradox. As mentioned elsewhere in the answers and comments, they do meet, momentarily, and simultaneously pass out with no other ill effects to themselves or the universe.
So, from this point I think we can apply some sort of Law of Least Effort: the Universe will only be destroyed to the minimum extent required to resolve the conflict.
When we look at the Jennifers, they could have met and had a lovely lunch together without causing any universal catastrophes. However, when you put the two of them together, they become a danger to the rest of the universe. The potential for any paradoxical conflict becomes higher because the two of them are together. Odds are most of those conflicts could be resolved without much hassle - millions of butterflies flap their wings without ever causing a hurricane, but it could happen.
What's more likely to happen during that hypothetical lunch between the Jennifers is that Old Jennifer is constantly having her history just slightly rewritten as Young Jennifer is influenced by what she sees to make small future choices differently. If Young Jennifer sees that Old Jennifer enjoys chicken salad even though she herself has never had a taste for it, perhaps she'll start to eat it earlier than she otherwise would have. Maybe this ultimately means nothing. But maybe Young Jennifer gets salmonella from improperly prepared chicken salad that she wouldn't otherwise have eaten, meet a nice doctor, break up with Marty and have an entirely different life. Would Old Jennifer fade away in the middle of the lunch? Probably. At least. It could be much more drastic. The entire future could be completely different, depending on how much relied on that particular choice.
Perhaps the entire future could fade away, with our time travellers in it. Whoops. Now we've started a cascade, because now the past point where they left from has to resolve the conflict of them missing, because the future they went to no longer exists. Maybe they'll just be gone, and that's that. Maybe not. Maybe, when everything is said and done, the whole of existence will be gone.
So, that's a rough idea of the mechanism at play in the paradox that could be created when the Jennifers meet.
It's a slightly different scenario when Marty is in the past and fading away. He's changed the future by interfering in his parents meet cute. He's fading away because he's potentially changed the future enough that it prevents his birth. This can be resolved completely by his fading away. Nothing else needs to happen to fix it - the future that he's from, for all intents and purposes, has been obliterated, but he's the only errant element missing from it, and there's a new future to take its place, the future from this new series of events.
What we don't see, but what is probably happening simultaneously, is that the DeLorean is also fading from the timeline as he is. If Doc still developed the time machine, and input the date in 1955, and managed to take Marty's place in the DeLorean (or some other helper did so instead), then what might be happening is that as Marty is fading out, the other time traveler and their version of the DeLorean could be fading in.
That could cause some cascading problems. Because now you're inserting someone else into the history that would have been doing different things that would not have been done in Marty's timeline. Probably that can be resolved by small changes to the timeline - after all, how much could be changed in a week - but maybe they can't, especially if that other person created conflicting interactions with the now missing and unobtainable Marty. I don't think you can assume that "the Universe" would keep whoever it was from going back into that time, but at the same time, maybe Doc was killed and no one went back in time in the new future. In that case, there's nothing left to fix, once Marty is gone, he's gone and the paradox has been resolved.
What I wouldn't expect is that Marty's disappearance would unwrite any of the impact he had had on the timeline - he existed in 1955 until he didn't anymore. His fading away happened at a specific point in time, if his fading away would have had a broader impact it wouldn't have just been him that faded but everything changed by his presence would have faded at the same time - notably the guitar, or as he faded, Marvin would have faded into place on stage since his hand would not be hurt. That suggests that there's no paradoxical loop by which he could cause his own undoing, and then undo that cause because he's no longer there to cause it. That's not how paradoxes work in BttF. If he faded away, the guitar would have dropped to the floor, because he had been there to hold it and then disappeared at that point in time.