Our rentals are in a remote, resort area, and we handle check in electronically--and almost never welcome a guest in-person. When the guest has signed our agreement and emailed it, we email back the codes to the home with map, directions, codes, area activities, and the check-out process. Electronic locks and lock boxes are economical ($35-$100) and can solve this. In your information page, you can indicate that for religious reasons, you don't respond on Saturdays, so the guest knows not to expect this. Maybe explain that from a cultural perspective, if they are foreign and ingorant of that tradition. Encourage people to receive the information electronically a week or so ahead of time. We also have paid staff who can help, but when we have "check out" on a big Holiday (American Thanksgiving, this year for an example) we blocked the following day so our staff member would be sure to have the Holiday off.
It works well for a whole-home booking, when you aren't sharing the space.
Hope this makes sense, and I think it would be great if you can figure out a way to observe your religion and welcome guests.