This is further complicated by the two phrases: "the US says" and "it says". One could argue that neither phrase is critical to its sentence. So let's look at the sentences without those phrases.
The targets could include military headquarters, command centers, as well as missile and rocket launch sites (that) were tied to the chemical munitions.
It's protesting the exposure of women's skin during the competition which violates Muslim teachings.
Now it is clear that the "that" in the first sentence and "which" in the second sentence are essential. It is even clearer that the clause in the first sentence is defining and the clause in the second sentence is non-defining.
So to sum, it up, I think that the major differences in the two clauses are defining versus non-defining and the additions of the almost parenthetical phrases "the US says" and "it says". In my view, the answer lies with both of these, but I can't be more specific.
Perhaps one of my colleagues can do better.
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