Except for the altar, which is usually the first thing you see here in the United States of America, when you walk into the Church, your description sounds like the way my parents talked about their old Church’s growing up in Ireland.
My father had a bird that flew everywhere he went, even to Mass and School, but for some reason, that bird always stayed outside.
Even here, when my parents were younger things like that occasionally happened. They didn’t have a lot of air conditioning then. They do now.
I do know a Priest who takes a dog with him everywhere he goes, but the dog never goes into the Church while Mass is going on.
For some reason, I think I would enjoy what you and my parents experienced. But, I am a Franciscan at heart, and I care very much for animals.
There is an old legend that St. Francis use to walk around with bells on his toes so that he could warn the crickets and ants and other smaller bugs that lived in the ground and grass that he was walking through so they could hear him coming and move out of the way so he wouldn’t step on them. I heard that when I was very young and have loved St. Francis ever since. I could understand someone like that, as I cared very much for God’s little creatures too. (except spiders, ugh!!!) , and I’m not real fond of mosquitos or fleas either. Other than that, I’m good.