We're here now and yes there are places you have to take your shoes off for temples as well as other places such as Kanazawa Castle in a specific building. We did eat at a Halal restaurant in Kyoto last night where upstairs had the tatami mats so shoes off. We also stayed at a ryokan in Hakone where technically shoes would not have been appropriate inside the room (you left them right inside your hotel room rather than communally like some other ryokans) and when you left the room you wore the slippers provided but that's similar enough to what you mentioned with visiting someone's house.
There are plenty of temples you can go into some have closed off areas sure. Just last night in Nara stepped inside a random one off the side of the road where you needed to take your shoes off. You'll see signs telling you when you'll need to take off your shoes and usually there is a specific spot they want you to stop at to do so.
One thing to note is that "temple" is used generally, by that I mean an entire area might be labeled and considered a temple but only specific buildings require shoes off. Nanzen-ji Temple in Kyoto for example had 1 area where you had to take off your shoes and they provided a plastic bag to hold them plus slippers to wear throughout the building. Ekando Temple in Kyoto also was shoes off but only in certain parts of the building.
Also temples also will tell you when you are not allowed to take pictures, some are you can take pictures of outside grounds but not inside this particular building but another oneis fine, some are inside this room but not that room.
The shoes both my husband and I are using are sketchers but they are well worn in that they are easy to take on and off even without unlacing at least for me, mine are arch fit ones.