Order 65 states:
Order 65 was one of the 150 contingency orders that the clone troopers of the Grand Army of the Republic were trained to carry out in the event of different emergency scenarios during the Clone Wars. Order 65 stated that if a majority of the Senate or the Security Council declared that the Supreme Chancellor—at that time Palpatine—was unfit for duty, the Chancellor was to be captured or, if necessary, killed.
But Mace Windu and the Jedi Council:
Thinking pragmatically, Windu concluded that the Jedi Council would have to seize control of the Senate in order to secure a peaceful transition of power from the Office of Supreme Chancellor to the Jedi High Council. Master Yoda feared where such a line of thought would lead the Jedi Order, but even Yoda himself was weary of the Chancellor's actions and seemed to agree, albeit reluctantly, with the idea of arresting Palpatine and stripping him of his office.
Here is the transcript.
MACE WINDU: I sense a plot to destroy the Jedi. The dark side of the Force surrounds the Chancellor.
Kl-ADI-MUNDI: If he does not give up his emergency powers after the destruction of Grievous, then he should be removed from office.
MACE WiNDU: That could be a dangerous move ... the Jedi Council would have to take control of the Senate in order to secure a peaceful transition . . .
Kl-ADI-MUNDI: . . . and replace the Congress with Senators who are not filled with greed and corruption.
YODA: To a dark place this line of thought will carry us. Hmmmmm. . . . great care we must take.
How exactly is that thinking pragmatically when they have Order 65 on the table? Not to mention that they aren't just talking about removing Palpatine, but taking over the Senate. It is not like there is no other option, there is an entire Security Council that seems like it was formed for just this purpose. The council is only loosely defined in the Wikia:
The Security Council was a group amongst the Galactic Senate that was charged with overseeing the security of the Galactic Republic.
Among the Security Council's list of powers was the authority to initiate Order 65, a contingency command instructing all units of the Grand Army of the Republic that the Supreme Chancellor had been declared a threat to the Galactic Republic and was to be apprehended or terminated if necessary. Unlike its counterpart, Order 66, Order 65 was never enacted.
But it seems like one would reasonably assume that the Security Council would be autonomous from Palpatine himself. Not only does this decision seem rather odd for the supposedly wise Jedi Council but it:
Leaves the door wide open for Palpatine to execute Order 66 and start the Great Jedi Purge.
It is also important to note that:
At this point the Jedi don't realize Palpatine is Darth Sidious. He's just another politician to them.
So, are there any other in-universe reasons why the Jedi ignore this option?