Wrong theme shows on homepage

Hi! I LOVE this theme, but I’m having an odd issue: If I (or anyone else on a laptop/desktop) am logged out, I see not just the wrong theme but blog entries that have been deleted! If I view the homepage logged in, it looks fine. This is not a problem with any other themes, and I have cleared my cache and tried it on multiple computers. Viewing logged out on mobile works just fine too, as does changing from “latest posts” to a static page. If you click a link it will give you a 404 error using the correct theme! https://cerysjones.co.uk
If you have any ideas how I can fix it I would be eternally greatful!