I haven’t done this particular ride but I have done a ton of riding in both Kansai and Kanto though I haven’t ever ridden a foldable; I ride a cyclocross bike and put paniers on for longer trips. Not sure about Shikoku, but in general riding is a great way to get around Japan. Drivers are generally pretty courteous, even though the roads can be pretty narrow. Also tunnels… avoid them if you can, but often you can’t. Make sure your bike is well lit and that you’re wearing reflective gear.
The one thing you want to be careful about is the weather. If you already live here, then you know, but in case you don’t, it’s currently 32-38C every day, and will remain so for the summer. I did a longer (1000km) trip in August one year, and it was pretty miserable, plus you can end up waylaid for a couple days by a typhoon depending on timing.
I can’t imagine that visiting a bunch of temples along that route would be at all offensive to practicing buddhists - people visit temples all the time and as long as you’re not being disruptive, I can’t imagine any problems. I’ve always felt more than welcome at temples. Sounds like a really nice way to see Shikoku!
One thing about a foldable is I imagine it might be easier to pack to bring on trains, assuming at least some parts of your trip will be on the train. Otherwise, buy a bike bag and get ready to disassemble and reassemble your bike for any parts of your travel that involve a train.
If you haven’t looked at it yet japancycling.org is a good resource for cyclists. I remember reading it before I moved here 20 years ago, and it had a lot of good info - not just routes, but things that might not be apparent if you haven’t cycled here before (e.g. bike bags).