Cathedrals, temples and shrines receive large numbers of visitors who hold none of the beliefs involved. The draw is explicable in terms of what these buildings were built to do.
They were built to produce specific effects
Religious architecture was designed to act on people directly, using height, light, proportion and sound rather than decoration alone.
Those decisions were made deliberately by builders with a clear intention, and the effects continue to operate on anyone in the space regardless of belief.
A visitor with no faith is subject to the same architecture as a worshipper, which is precisely what the architecture was designed to accomplish.
The acoustics are unlike anything else
Large stone interiors produce long reverberation, which developed alongside the music written for them and remains audible in ordinary conversation.
The effect lowers voices without any instruction and gives the space its characteristic quiet, which visitors adopt within a few steps of entering.
Modern buildings are acoustically treated to reduce exactly this, so the experience is now genuinely rare outside religious buildings.
Nowhere else is free, quiet and open
In most towns, religious buildings are among the only interiors a person can enter without paying, buying something or explaining why they are there.
They are also among the few where sitting still for an extended period attracts no attention at all.
That combination has largely disappeared from public space, and people use these buildings for it whether or not they engage with anything else there.
Continuity of use is visible in the fabric
Worn steps, repaired stonework, memorials spanning centuries and accumulated objects make the length of use physically apparent.
Visitors describe this as atmosphere, and a substantial part of it is the visible evidence of continuous human attention to one place.
Reconstructed and newly built sites frequently lack it, which is why replicas rarely produce the same response despite matching the design.
Managing both audiences is the practical difficulty
Sites depend on visitor income for maintenance while remaining places of worship, and the two uses conflict at predictable points.
Common arrangements include reserving areas for prayer, closing during services and asking for silence at set times, all of which are negotiated locally.
Where visitor numbers are very high, the site can become primarily a monument in practice, which is the outcome most communities responsible for these buildings work hardest to avoid.