Epicureans thought politics was a needless cause of stress and anxiety. The masses are incurably deluded, and the powerful are incurably corrupt, so it’s best to withdraw from the state, set up your own philosophical commune, and pursue the good life privately. Some Epicureans did attempt some outreach, though. Diogenes of Oeneanda paid for a large wall to be erected outside his city, inscribed with Epicurus’ teachings, to spread the word of his philosophy. (Quoting from the website philosophy for life.org).
The problem we face is that the scope of politics in Ancient Greece was rather limited. You could feasibly ignore it, unless a war visited your doorstep. The size and reach of government in modern times is quite different. Government is useful and important and has improved the lives of most people. But it’s reach is such that you simply cannot ignore it. The good that it can do can easily be reversed by those with different ideologies.
If everyone ignored politics then the bad actors would hold the stage unimpeded, like Hitler or Stalin. This is the dilemma facing Epicureans. It suited politicians like Margaret Thatcher to have a supine public, whom she viscerally loathed. Had people stood up to her the dire changes in the UK, some of which were necessary, would have been more moderate.