I Never Read Those Books - Tumblr Posts
I'm going to be a heretic and say that the Jedi's problem wasn't that they were involved the Senate, it was that they weren't involved enough in the Senate. The Jedi should have moved out to the Unknown Regions if they didn't want to deal with the responsibilities of the Republic. They should have involved in politics by voting for leaders, running for election and utilizing their representation to push for their interests and agenda.
"but they didn't want to be involved-" look here people, you do not choose to get involved in politics. Politics involves everyone; you have a choice to play or not play. There is no option to opt out. By not playing, you forfeit the game to your opponents, and you lose before you begin.
That's how Palpatine wins. He sets the game, and the Jedi forfeit; they were doomed to lose from the start.