Times of tensions and distance between the Jedi and the Republic?

The Jedi have often been criticized in the last decades of the Republic and after by later characters for having attached themselves too much to the Galactic Republic and for letting their actions being dictated by the Republic even when the Senate or Supreme Chancellor's orders were questionable or outright wrong, which the Banite Sith and Darth Sidious above all used to their advantage to gain power and destroy the Jedi.

But what are the times and eras where the Jedi were more distant and even defiant towards the Galactic Republic and its decisions and actions, having kept some distance and independence or at least autonomy for themselves, and with them contesting or refusing to follow the Republic's actions?