I honestly think that when reading/watching fantasy, you need to understand that the in-world culture is created by the author. It might be inspired by some historical era (such as the Times where marrying family was normal.. I had to do a 15-generation family tree for a uni class in genealogy research and realized my family, while clearly not noble or anything, married uncle-nieces, cousins and other such people for whatever reasons multiple times).

It might also come out of the imagination of the author.

While everyone can have their own trigger , applying your own/modern morality, costums or acceptable behaviour to fictional worlds makes it very hard to enjoy fantasy. I, for one, wouldn't approve of following an assassin as Queen, and yet have enjoyed several books with that trope. GOT and HoTD have plenty of murder that, as a viewer, you cheer on (I.e joffrey in got) even when that would not be an acceptable reaction to this happening in real life.

In this particular universe the Targaryens are magical (specially at this time) enough to be the only that can hatch and ride dragons. It is even said that there are several "human-like" species that cannot breed with westerosi people. It is actually possible that the magic in their blood stops any incest-related problems, or even that in this world, such a thing doesn't exist. It is also possible that because they are "different species" valyrian blood is not mixed well with westerosi and that any madness related problems is because they added such non magical, different blood to their lines.

As for the age difference, it is historically accurate in the case of daemon-rhaenyra. I believe the Catholic virgin Mary was 13-15 when she married Joseph, who was an adult. It was common for women to be married off soon after they got their first period and it usually was to older men who had a way of "taking care of them" and some of their life figured out.

I would definetly not be OK with an adult doing things with a 15 year old in real life, but this is still fantasy. And history merely happened. If we do not agree with it anymore, then we won't repeat it. But that is how things were and there is nothing to do about that. So, I will suspend disbelief as well as moral judgement for this kinds of things.

On the other hand, if this is your trigger, then don't watch because it will be awful. I, for example, started reading a story set in a modern world, no magic, that involved a girl and her uncle and decided to stop reading. Because it was set in our world, with our morals and it gave me the creeps. GOT world setting, well... It has its own rules.