I'd do what the thinset directions say on the bag regarding drying time. If the thinset is modified it takes air to dry. If it is only unmodified thinset it dries via chemical reaction I believe. I have done several tile jobs in my home and always waited longer then the instructions say to let the thinset dry, because I worry.

Regarding the plastic, I would not do it. Maybe someone with experience will tell you different.

I wonder if I remove plastic after showers to allow air drying.

As soon as the tiles are dry (i.e. not moving) you can grout. I use rapid set often for repairs in time sensitive situations. 4x4 ceramic tiles will usually suck out the moisture in the thinset quite quickly even with regular thinset depending on the substrate you are re-tiling. A plastic sheet would work well to keep the water off the repair. I don't see any problems with your plan. And yes removing the plastic will allow to air to circulate better.

Once you grout, try to keep the wall repair completely dry for about 48 hrs if possible so you can seal the grout properly.

And make sure that the substrate being repaired is sound and suitable for tile.

Not much to add to the other replies. Thinsets have different chemical makeups and those differences factor in to cure time before grouting. So as has been mentioned, read the instructions on both the thinset and the grout bags.

Tarping with plastic? Have at it. Been there, done that, with bathrooms that could not be taken out of commission.