Copper is an anti-biological. For example: copper oxide is used in anti-fungal treatment for trees, but is known to kill beneficial bacteria in the soil.

Copper is listed as the main active ingredient in “anti-fouling” paint used on the bottom of ocean going boats to keep barnacles and plants from taking hold.

Based on that information I would believe that copper cups are at least somewhat anti-bacterial.

However, things that kill bad bacteria also kill good bacteria. Could this affect the gut biome?

I don’t worry about anti-bacterial soaps, cups, etc. Your immune system needs a little exercise to stay healthy. Just like the rest of our body does. Don’t waste your money.

I can dispel most of the other claims off the top of my head also, but this note is already long. Let me know if you want to learn more.