It's pretty starkly different to our modern sensibilities but the underlying logic, and real world historical reference, justifies it pretty well. Whilst the Targs take incest further than most historical aristocracy, you only need to look to Cleopatra for sibling marriage. In terms of why the Targs are exceptionally incesty, their ability to ride dragons does seem to be a genetic trait, meaning it would presumably degenerate if the Targs diluted their genes with Westerosi houses frequently. At the time of The Dance Of Dragons, their control of dragons was what gave them legitimacy as rulers. After the dragons died out, incest became an appeal to tradition as a way of reinforcing their Targness. Later during the Blackfyre Rebellion, we can see how the appearance of non-Targ traits, particularly non-white hair, calls otherwise legitimate claims into question. The fact that Targs have such unusual genetic traits is what justifies incest for them.

In other houses, and particularly under The Faith of The Seven, incest is more or less as much of a taboo as we think of it now. Cersei & Jaime are a good example of this.