Can 3D printing make rubber buttons?

Yes, "rubberized" not rubber. You would use TPU [thermoplastic polyurethane) which is rubberised when cold but can be melted by the hot ends. I haven't printed with it myself (it's FDM, but needs very, very slow feed and a special head) but many of the Chinese board houses will do this for you. I used JLCPCB ( https://jlcpcb.com/3d-printing?from=3DP) but there are quite a few if you shop around such as www.hubs.com. Most can produce parts in esoteric and expensive materials including SLS (metal) printing!

The advantage of using the professional boys is you get much better quality printers that will print a well-designed model without all the worry of ending up with a blob of plastic on the bed or twisted plastic noodles everywhere. 🙂

I would suggest you check your models by printing them in PLA first to make sure your model works properly. A complex model may require a dual-feeder that can make "supports" from a water soluble plastic like PVA.

Commercially produced "rubber" buttons are made in moulds but this won't be a reasonable option for just a few parts.

Hello, my friend. I haven't made such a detailed object before, but I think it's doable. PLA or TPU should both work, but you need to pay attention to layer height and print speed. The hole in the middle might be a bit tricky. Do you need a lot of them? Otherwise, it might be better to just buy them. 🤣 🤣