It seems absurd to think that a tax dispute between the world's biggest trading bloc and a U.S. technology giant with an almost cult-like following could break up a political and trade alliance born after the most devastating war ever. But that's exactly what the fight over what taxes Action Alerts PLUS holding Apple (AAPL) - Get Report  should pay or not pay could end up doing.

The clash highlights the many divergences at the heart of the European Union at a time when the EU is fighting off increased challenges like the U.K. Brexit vote and the backlash against eurozone austerity. The EU's two-year competition investigation into Apple's tax position in Ireland concluded that the tech titan got as much as €13 billion ($14.5 billion) of undue tax benefits from the Irish government.

The full explanation is in the European Commission's press release, but the EU basically accused Ireland of letting Apple divert profits to two subsidiaries that had no operations, no employees and no real head office. This meant the company paid virtually no tax on profits.

Although the arrangement ended in 2015, the EU said this tax treatment amounted to illegal state aid for Apple. Authorities want the company to pay Ireland back taxes for the 10 years prior to 2013, when officials first requested information about this case.

Not surprisingly, Apple plans to appeal the decision -- and its shares hardly moved on the news because (as Jim Cramer pointed out) this is a company with around $200 billion in cash. Thus, the back taxes that the EU wants AAPL to pay only amount to just a little over 7% of that.

The U.S. technology giant also fired the first salvo in what could turn out to be a political struggle that either makes the EU stronger or brings it to the brink of a breakup. In an open letter, Apple called the European Commission's move "unprecedented, and it has serious, wide-reaching implications. It is effectively proposing to replace Irish tax laws with a view of what the Commission thinks the law should have been. This would strike a devastating blow to the sovereignty of EU member states over their own tax matters, and to the principle of certainty of law in Europe."

Ireland has already announced that it won't ask Apple for any additional money, with the Irish finance minister putting it rather poetically: "To do anything else would be like eating the seed potatoes." The country has gotten lots of U.S. companies to establish their EU headquarters there due to Ireland's low tax regime.

However, this dispute is just beginning. Expect more public figures to step into the limelight and either defend the EU's stance or side with Apple and call for a withdrawal of powers from the "unelected, faceless Brussels bureaucrats," as the pro-Brexit British media dubbed the European commissioners.

In the United Kingdom, some newspapers that supported the Brexit were quick to side with the U.S. tech giant. A story in The Telegraph about how U.K. Prime Minister Theresa May would welcome Apple to Britain was the most viewed tech item on the paper's website. Meanwhile, business newspaper City AM wrote that a post-Brexit Britain could become a "new sweetheart" for America as the Apple issue opens a rift between the United States and the EU.

Depending on how this battle unfolds, the EU could either emerge as a pro-consumer hero or reinforce its image as an overbearing, interfering supranational entity that dictates unpleasant measures to member states. Expect Brussels to fight hard for the former option. It has no choice, because in the current political climate, the latter one could mean the EU's end.

Editor's Note: This article was originally published at 9 a.m. EDT on Real Money on Aug. 31.

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