I just went to arc flash class and it came up under "Shock hazard analyzes" Table 130.7(C)(9)(a). That you need to use gloves when checking ANYTHING ANYWHERE over 120v. Is this correct?
Does it mean that I can troubleshoot a 120v or less control circuit without them or other protection if arc flash rating is Cat 0.

Thanks
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Arc flash rating and shock potential are two independent issues. Something can have a hazard/risk category of 0 and still be a shock hazard (that's pretty common, actually.) 130.7(C)(7)(a) states that "employees shall wear rubber insulating gloves with leather protectors where there is a danger of hand injury from electric shock due to contact with energized electrical conductors or circuit parts." Arc Flash is handled in section b and is totally independent.

Almost correct. SOME table:entries require rubber gloves to meet arc flash rating using the table method. If you are not using the tables then gloves are sometimes an option depending on the hazards. For instance at 69 kv rubber gloves are specifically prohibited. See IEEE 516 for detailed shock protection requirements.

When the original post is citing 120 V, I don't think they were really thinking about 69 kV examples.

Agreed. The reason I use 69 kv as an example is that the shock sections of 70E specify various methods (gloves, insulated tools, bare hands) while ignoring others, particularly cover up, and do not give any guidance at all as to what is actually required. Many standards, including old ediyions of IEEE 516, almost seem to suggest that gloves are always required at every voltage and for every scenario when in fact there are multiple options and in many cases gloves are not the best option, nor even an acceptable option at higher voltages. So I use the case of 69 kv or higher to jar the "gloves only" crowd into recognizing that gloves are nkt always the one, true answer tl everything. Usually insulated tools are the best option for under 300 volt conditions.