Star Wars was built in a massive galaxy with thousands of years of history and characters, but the most popular era is that which spans the time period from The Phantom Menace to The Rise of Skywalker. That period of galactic history was defined by the actions of Sheev Palpatine, known to many as the Emperor or Darth Sidious. But his magnificent plans during the Clone Wars had a huge hole in them that may have cost him everything.
After the Jedi believed they had destroyed their enemies, the Sith retreated into the background of galactic dealings. They began a long term plan to undermine both the Jedi and the Republic, giving them the upper hand before the either group knew what was happening. The finals stages of this strategy were implemented by Darth Sidious, a powerful Sith Lord who manipulated the entire galaxy.
A senator from Naboo, Palpatine connived his way into becoming the Chancellor of the Republic. He orchestrated the entire Clone Wars, creating both the droid and Clone armies. Palpatine also created the conditions required to instigate the conflict, slowly amassing power and control throughout the war thanks to the instability. By the time it was all over, the Jedi were all but destroyed and the Republic had become the Empire.
The war ended with the implementation of Order 66. This command was programmed into all Clone troopers via control chips implanted in their heads at the earliest possible stages of development. Once the order was given, the Clones turned on their Jedi allies in combat and murdered them. Only Clones like Wolffe, Gregor and Rex who were able to remove their chips avoided this fate.
While all of the Clones were programmed for Order 66, none of the droids serving on Republic ships appeared to be. The final episodes of The Clone Wars detailed what happened to Ahsoka Tano in the immediate aftermath of Order 66. With the help of a group of Astromech droids, Ahsoka was able to free Captain Rex from his control chip and escape their pursuers. Without the Astromechs, it's unlikely any of that would have been possible.
Both Ahsoka and Rex would go on to play huge roles in the Rebellion against the Empire. The movement's strength would grow over time, making them a credible threat to the Emperor's plans. Without the support and guidance of Clone War veterans like Ahsoka and Rex in its early stages, it's quite likely that the Rebellion would never have gotten off of the ground.
Beyond that, not programming Order 66 into Republic droids allowed one of the greatest heroes of the Clone Wars become a greater hero in the Rebellion. R2-D2 saved numerous Jedi, Clone and Rebel lives over the years with his heroic actions. Almost countless missions would have failed without him. But as a droid operating on a Republic ship, he would have been subject to the Order 66 programming had it been implemented on all droids.
Ahsoka, Rex and R2-D2 all played their respective parts in defeating the Empire. There was a real chance that the Rebellion could have been stopped before it started if had Palpatine bothered to program Order 66 into Republic droids during the Clone Wars. The irony was that putting this small piece of programming in place would have been incredibly easy to implement and even easier to cover up. Overlooking the importance droids ultimately cost Palpatine his Empire.