Does CICO still apply to people who are insulin resistant?

I'd definitely avoid Taubes and Fung.

And yes, CICO still applies if you are IR. Why is low carb recommended (by some)? Insulin is not bad (normally), it's how your body moves things around, such as glucose to muscles and (if it needs to be stored), fat cells. However, when someone is insulin resistant, their cells do not recognize the insulin and thus it has trouble storing the glucose or using the energy from it effectively. (Ironically, this means it is harder to store fat from carbs, but normally the person is also eating lots of calories from fat and continues to gain.)

When you can't move the glucose where it needs to go, you get high levels of sugar in your blood which can be dangerous. At first, of course, IR does not prevent the body from doing this entirely, but requires extra insulin to do so, and then more and more and so on. Often what happens is that the body overreacts and when blood sugar is moved from the blood it basically plummets, and you get those spikes and crashes of energy that some experience.

Anyway, the reason for the IR epidemic is obesity -- many, many people who wouldn't otherwise have it will develop it if overweight or obese (others are lucky and do not). A much smaller number of people (increasing as we age) can get it even if not overweight. If your family members developed IR with obesity or excess fat, then staying a healthy weight will likely be the main thing you need to do.

For addressing IR, mainstream medical recommendations are not that you need to go low carb, but that to avoid blood sugar spikes carbs should be eaten with fiber and often protein and fat too. Avoid refined carbs on their own or just with fat is often a recommendation. And if overweight, lose weight. Merely losing weight very often brings it into remission (for example, you could eat plain potato or a piece of bread without a problem like a person without IR).

Low carb does not bring T2D/IR into remission, but it prevents the symptoms (the blood sugar spikes) which if unrestricted can cause harm for someone with this condition. But if you eat the carbs, the condition returns (unless you also lose weight and then often the remission happens).

Low carb is not a diet that works for everyone, as it assumes you will be satisfied and sated eating that way. Some are, and often those with IR more than others since they were possibly not getting adequate energy from carbs as compared to how others process them. But not all, and even many who like low carb find it helps to calorie count.

I think eating a generally healthy diet is probably a good idea, but you should focus on what you find satisfying too, and no need to do low carb if you don't want to just because some family members have IR (there are alternatives even if you have IR and for most losing weight and adding exercise (which also helps with insulin sensitivity) is the main thing).

I never went low carb but put my diabetes in to remission from significant weight loss.

Fewer calories in, smaller body, the pancreas can now keep up with my insulin needs.