There are some indications that relative inequality creates vocal anger and unrest, however, it generally takes quite low levels of actual living standards (or physical security) before masses of people become willing to actually risk their lives in violent overthrows of the regime.
Historically, "Bread and circuses" is sufficient to keep disgruntled poor masses just disgruntled but not revolting; regimes get overthrown either when the rulers can't provide bread anymore, when they do unbearable physical harm (e.g. disappearances, torture, etc), or when an external force comes in. And currently it's not a big burden on the economy to just provide lots of cheap food and entertainment for everyone to pacify them, that can be done with just a few percent of GDP.
Historically, "Bread and circuses" is sufficient to keep disgruntled poor masses just disgruntled but not revolting; regimes get overthrown either when the rulers can't provide bread anymore, when they do unbearable physical harm (e.g. disappearances, torture, etc), or when an external force comes in. And currently it's not a big burden on the economy to just provide lots of cheap food and entertainment for everyone to pacify them, that can be done with just a few percent of GDP.