There really isn’t a consensus or a definitive answer to these questions. Some people are extremely strict, and others (like myself) are much less strict. The best thing you can do to decide for yourself is to ask people why they have come to that conclusion about something breaking or not breaking a fast, and to learn more about the biology of fasting from reputable sources (such as peer-reviewed scientific papers).
The generally-agreed point of fasting is to let insulin drop back to baseline and stay there, and to force your body to burn through its stored sugars and start burning fat for fuel. Consider how much each supplement would actually affect those biological processes, balanced out with the benefits of taking that supplement, and make your decision based on that information.
“Breaking a fast” is really a gradual process. All of the biological processes involved have more like a volume knob, where they get turned up and down, not like a switch where they are either on or off. So where you consider the fast to be “broken” is really a judgment call. That is why you get so many different answers. Different people make the judgment call at different points.
My opinion is that anything under about 50 calories will have an effect on insulin, but it will likely be minimal and short-lived. If you must have a small amount of something (like cream in coffee), it will be better if it’s fat rather than carbs, because it will have less of an effect on insulin. Artificial sweetener may have an insulin effect for some people, but again, minimal and short-lived. But the maybe 0.1 calories in a supplement capsule casing? That will have no measurable effect on insulin at all. Again, this is my opinion — this is where I make the judgment call. You may choose to make it differently.
(However, I will say confidently that taking table salt & Lo/No-salt absolutely does not break a fast, not even according to the strictest water-only people I have ever heard. In fact, it’s really dangerous and potentially deadly to do extended fasts — anything much more than one day — without taking sodium & potassium. Who is saying they do break a fast?)
The only way to really know would be to use a glucose meter and figure out your fasting baseline and go from there. If the items don’t change your blood sugar, you’re probably not breaking fast. I’m NOT a medical doctor so take all this with a grain of salt. I did use glucose testing when I was being checked for hypoglycemia.
Dr. Berg says anything below 25 calories should be fine.