It never feels like it at the time, but you're better off winding up at a workplace that values your contributions over your political connections.
Perhaps even more so than places with a formal structure.
However, could you explain what you mean with 'political' in this context? Because 'political connections', in my mind, also includes reputation and knowledge of competence. And that doesn't seem like a bad thing.
Even the example you give requires reputation management, as opposed to merely raising a good technical argument at the time (as a new person on the staff).