Star Wars: The Bad Batch season 1 reintroduces the deserter clone, Cut Lawquane, and reveals that like Clone Force 99, he wasn't affected by Order 66 - but why is that? Picking up events almost exactly where Star Wars: The Clone Wars leaves off, The Bad Batch is exploring the earliest days of the Empire's rule over the galaxy through the eyes of the Bad Batch - Hunter, Wrecker, Echo, Tech, and Crosshair. Beginning with the delivery of Order 66 to the clone army, The Bad Batch shows how this order not only turned the clones against the Jedi, but altered their personalities to make them completely obedient to the Empire.
In The Bad Batch's latest episode, Clone Force 99 (now without Crosshair, but having added Omega), flee Kamino and seek out an old friend, Cut Lawquane. First introduced in The Clone Wars, Cut is a clone trooper who deserts from the Republic Army and settles down with a Twi'lek, Suu Lawquane, and her two children, Shaeeah and Jek. His decision to abandon the Republic doesn't sit well with Captain Rex when he discovers Cut during a Clone Wars mission to Saleucami, but in time, Rex comes to understand that Cut has found something he wants to fight for more than the Republic - his family. Cut's choice is unusual for a clone and it hints at an independent streak within him, but is that enough to defy Order 66?
In The Bad Batch season 1, episode 2 "Cut and Run", Clone Force 99 finds Cut and his family still residing at their farm on Saleucami. They learn that Rex has recently been there and informed Cut about the clones turning on the Jedi. Rex also revealed to Cut the existence of the inhibitor chip, which is what allowed the Empire to take control of the clones via Order 66. It's likely Rex told Cut about the chip as a warning to get his removed, since as a regular, unmodified clone, Cut surely has a chip inside his head like all the others. And yet, Cut was obviously unaffected by Order 66, so does his chip simply not work? It's possible, and perhaps a malfunctioning chip is what helped him to desert in the first place. However, it's more likely the case that since Cut is a deserter living in secret, he simply didn't receive the order.
While the chip is integral to the Empire's control over the clones, the actual "Execute Order 66" command is still the necessary trigger. In addition to Palpatine appearing via holovid to various clone commanders, Tech says in The Bad Batch season 1 premiere that their "comm channel is repeating one directive: Execute Order 66." This explains how even those clones who are not shown receiving Palpatine's message were still triggered to carry out the order. In the case of Clone Force 99, their mutations prevent the order's brainwashing from taking hold; though it depends on the extent and type of mutation, as Crosshair does comply with Order 66 to a degree, and his chip is later manipulated to become more effective. Still, Crosshair receives the command just as every other clone within the army, but as a deserter, there's no Republic comm channel to reach Cut.
Without receiving the command to "Execute Order 66", it seems that Cut's inhibitor chip isn't triggered. And as the order has already been given and worked, it's doubtful the Empire would ever need to resend it. Even if they did, it's still unlikely the order would reach Cut. What's more, Order 66 doesn't function exactly the same way as other trigger phrases in pop culture, like The Manchurian Candidate or in the case of Marvel's Winter Soldier, where anyone with the trigger phrase can activate the subject. Rather, Order 66 appears to be a command that can only be given by Palpatine himself, meaning Cut runs little risk of his chip being accidentally triggered in the future.
That being said, were Cut to somehow encounter the Order 66 command and have it activate his chip, there's still a chance he could resist its impulse. While rare, there are cases of clones struggling against Order 66. For example, this what happens to Rex, and it's arguably his attempts at resisting that allow Ahsoka the time to remove his chip and save them both. Cut has already displayed an independence that's unusual for a clone, and it's not impossible to believe his strong will could override his chip. Even so, it may still be wise for Cut to have his chip removed, and as Rex will later help other clones do just that, Cut will almost certainly have the chance in the future, leaving him free to live his life as he please.