How much is the focus on bastardry odd? The Blackfyre legacy I get but even in pre Targ times, the Storm King is I insulted by an unmarried bastard brother but not a man married twice to his sisters?

Well, think about it sociologically. 

Any society in which the means of production, as well as all political power, are distributed and redistributed on the basis of marriage and birthright is going to have a huge problem with bastards. Bastards have alternate claims of inheritance as the sons or daughters of the people who claim them, they come from outside the boundaries of dynastic marriage alliances, and they threaten the settled principle of primogeniture.