For Osha, I only see a chemical list for gloves, for tools I don't see a list. If you are required to wear gloves or other PPE, the company should have proper training and/or documentation for the use of PPE (Personal Protective Equipment). I know it sounds kind of silly (how do I use gloves) but it is required.
General Statement of Glove PPE from Osha
For hand protection, there is no ANSI standard for gloves but OSHA
recommends that selection be based upon the tasks to be performed and
the performance and construction characteristics of the glove
material. For protection against chemicals, glove selection must be
based on the chemicals encountered, the chemical resistance and the
physical properties of the glove material.
The above link/document has lots of details on PPE.
I don't think there is any hard rules on glove use. For starters, whatever tool is being used, look at the manual to see if glove use is forbidden. It should be clearly marked. Usually there is a safety page that shows what PPE equipment should be employed for the operation of the tool.
Also, as others have pointed out in the comments, use a glove that fits and is right for the job at hand.