How did the brother sister Targ marriages keep going on with the Faith of the Seven still there for a little while even after the death of the dragons? What do you think was the Faith’s policy on that so that they didn’t look like hypocrites the public? Or do they just not care (what the smallfolk think i mean)

Over a hundred and fifty years of precedent smoothes things over somewhat. By that point, both the Faith and the smallfolk have come to see the Targaryens as something a little above human – hence the emphasis on the Targaryen “look.” 

Also, if we look at the Targaryen dynasty after the death of the dragons, incest becomes less frequent: Aegon III had his kids with a Velaryon, then you’ve got the bachelor King Daeron I and his chaste successor Baelor, then Viserys II was married to a Rogare. Aegon IV breaks the trend, but he’s not very popular anyway. Then Daeron II marries a Martell and his kids all marry outside the family, as does Aegon V. Only Jaehaerys II marries a sibling in the next generation, and then Aerys II does the same, and they weren’t very popular either. Rhaegar marries outside, and that’s the end of the line.

So really the Faith only has to deal with this problem three times in a hundred and fifty years, so it’s not a constant tension.