The difference with oil inflation is that it also directly boosts revenues in oil-producing Middle Eastern countries.

Consequently, they can offset core staple inflation (and usually choose to) to decrease unrest.

It's core inflation without high oil prices that torpedoes their fiscal options.

Perhaps it makes it less likely in the middle East, but it makes it much more likely in countries vulnerable to both oil & food price inflation.

The immigration crisis caused by Arab spring toppled many governments in Europe.

If a similar set of crises happened in the Americas it would make the US's illegal immigration situation much worse.