Oil often comes up in Middle Eastern geopolitics, but in a sense I feel like it rarely comes up directly enough. For starters, these market moves are at least decent evidence that observers who are neither "hawks" nor "doves" but who do have money on the line feel that bombing makes the region less stable rather than more stable. More straightforwardly, they're also just a sign that war could have a meaningful deleterious impact on the American economy. Higher oil prices are a negative supply shock to the United States that would slow job growth and reduce real wages.
I'm not going to pretend that cheap oil is some kind of decisive consideration. There's a strong case for not bombing that has nothing to do with oil. But the potential negative impact on the American economy is something hawks should address, and the predictive aspect of the oil futures markets is another thing hawks should address. The Arab League seems to think on a political level that bombing would be destabilizing, and oil markets seem to agree.