Look at the EU, NATO and other US alliances (e.g., with Japan). They are connected held together by values. They are very imperfect and corrupt, but these alliances have lasted so long because there is no way, for example, Germany is attacking France again. It just doesn't make any sense, because of the values.
International relations are fundamentally (but certainly not wholly) anarchy, but anarchy doesn't exclude values - perhaps it makes them even more powerful, relatively. As some have said, to a great degree, right makes might.
In practice, blowback is one result of ignoring it: The US supported the Shah, a brutal dictator in Iran. When the Shah lost power in ~1979 - well, you can see that the US is still paying a price. The US supported some unsavory people to fight the Soviets in Afganistan; some of those people became Al Qaeda. The US armed and trained brutal right-wing militias in Central America to suppress enemies; some of them became today's Central American drug gangs. Meanwhile, while the US promotes democracy and freedom, it draws many, many into its orbit around the world.
Didn't the US overthrow many democratically-elected governments (usually because they were leaning towards communism/the Soviets) and install undemocratic dictators in their place?
Coincidentally, here is an article that very issue in US property markets: