A more favorable interpretation would be that the church consists of more than just its worldly parts; its place and use are also part of its identity. Even if you'd completely rebuild the church building, the other parts of its identity would persist. Therefore, the "ship of Theuses" argument doesn't apply, as, in this case, we would never replace all parts of [the identity of] this church.

It feels like you’re referring to the “ship of Theseus” as an argument that the identity does not persist…

It’s not.

It’s a hypothetical designed to call attention to the exact thing you’re saying: that potentially identity is more than the specific physical parts.

I gave my differentiating factor..

Yes it's my take on the ship of Theseus problem.

In that problem we re asked to consider if a ship with all it's parts replaced is the same as the original..

My argument is that so long as the ship is being used for the same purpose by the same people then it is. Without a purpose, wood in the shape of a ship is not even necessarily a ship

Things are more than just their physical form.

Our own bodies are ships of Theseus. I've read once that every atom in our bodies are replaced in 40 years. In 40 years, our bodies change a lot and so are our minds. What make Theseus' ship the ship of Theseus, is that Theseus is the owner of the ship. Ownership is a social convention, a construction of the mind.

What makes Notre Dame, is that people generally agree it is still Notre Dame. If hypothetically we were in a time of modernism craze, and that our government decided to rebuilt it in some modern style (there actually was proposals like that), it would still be the people who makes it Notre Dame de Paris or not.