Not US but in Canada my old employer attempted to have me sign a new contract for a change of role stating I would get explicit allowance if doing any other work including volunteer work. And to note the other commenter volunteer work was specifically noted.

Needless to say I took that as a good sign to move on :)

My current employer has a much more reasonable policy that I can't work a second job when on my scheduled hours with them.

Probably not. It would certainly be exceptional if anyone actually has this in an employment contract. People are bringing this sort of thing up because of vague language in their employment contract or employee handbook that doesn't explicitly list every allowed/disallowed activity. To put it another way: "It doesn't say I can do this, so it must mean that I can't." It's... not a reasonable interpretation, IMO.

No one is going to prevent you from volunteering at a soup kitchen unless you're trying to do it during normal working hours when your employer expects you to be working for them. And in that scenario, lots of employers in the US actually have additional PTO specifically for doing charitable work for some number of hours per year, i.e. you can do it during work hours and get paid for it.

I have not seen such a contract. I have seen employee handbooks/policy manuals that explicitly require written permission even to volunteer for charities outside of work.