Trotsky is claimed to have said:
"You might not be interested in war, but war is interested in you"
J.R.R. Tolkien expressed a similar sentiment:
“It needs but one foe to breed a war, and those who have not swords can still die upon them.”
In organizational theory, politics is defined as a means of allocating scarce resources. If people are not interested in politics, then they are either not paying attention, or more likely we need to dig a bit deeper.
People who are not interested in party politics might be like the citizens of "People's Republics" in the 20th century. They were corralled to vote in elections where the Party candidate won with 98.9% of the ballots, and knew with utter certainty that their desires counted for nothing in the greater scheme of things. Today in Western liberal democracies, we are seeing something similar. First written about in a book called "The revolt of the elites", people in the political, academic, bureaucratic and crony capitalist class have essentially rigged the system against the rest of the voting public, corralling profits but "socializing" losses (i.e taxpayers absorb the results of bad decisions).
In the case of the People's republics, politics as a means of allocating resources was pushed underground, and black markets, cynical corruption of officials all the way up and down the line and sheer criminality was the rule of the day. One common saying in that era was "They pretend to pay us; we pretend to work". The collapse of communist regimes was accelerated by the hollow economic structure as people worked essentially underground for their own ends, rather than for the State.
In Liberal Democracies, we see an incoherent rage with is expressed in Europe by things like the Brexit, the rise of Nativist parties in major European countries and anti immigration/globalization backlash. (as a footnote, most nativist parties in Europe are incorrectly called right wing by the press; a look at their political platforms as published reveals right away they are far left National Socialist parties)
In the United States, we have the spectacle of anti establishment candidates like Bernie Sanders almost winning the Democrat nomination, Donald Trump wining the Republican nomination and "third parties" like Garry Johnson of the Libertarian Party and Jill Stein of the Green party polling in double digits (in the past, a third party candidate with 2% of the vote was an outstanding result).
Less often spoken of is the erosion of the Rule of Law in the United States and more open corruption by government officials. We also see people being strung along with broken promises, for example State employees expecting a government pension might be in for a shock: Government pensions are estimated to be unfunded by 3 trillion dollars and that is outside of the Federal or State debts.
So a society where people are uninterested in politics due to the real or imagined idea that their preferences are not going to be accounted for will devolve into a lawless society, where social cohesion devotes into family groupings, quasi-criminal organizations and corporations capable of using bribes and other crony capitalist tools to remain afloat. People are still allocating resources, just outside of the official hands of the State. Politics outside of crime will be more like "office politics" rather than party politics.
As a counterpoint to this parade of negativity, if politics is the means of allocating scarce resources, it is theoretically possible to go beyond politics in a post scarcity society. Since social, political and organizational forms will be changed beyond all recognition, this period is sometimes considered a "mundane singularity" (term coined by Brian Wang of NextBigFuture).