Someone was wrong.

Even modern appliances frequently don't have grounded (three prong) cords if there is no exposed metal, etc...

If your older cords are in good condition, no fraying, cuts, burned spots, etc... and the cord is securely connected at the plug and appliance ends, they should work fine.

If you want extra protection, make sure whatever receptacle you plug them into has GFCI protection.

If the wiring and appliance is indeed in good condition, it should be as safe now as it was in the 20s.

Thank you for the replies! I really appreciate the info.

In fact, it's safer to plug it in to a modern outlet than into an old one. They aren't matched sets you know.

Okay... but to be fair - older appliances are almost always metal and not grounded and would guess aren't UL approved in many cases. Don't expect the same product safety awareness as we have now.

Use them on a GFI and unplug them when you are done.

I have a very cool old waffle iron that I still use - but only on a GFI outlet.