Two practices at Puri put pressure on assumptions about what a sacred image is, and they pull in opposite directions.
The renewal of the bodies
The images of Jagannath, Balabhadra and Subhadra are made of wood, and wood does not last. At intervals of twelve or nineteen years, whenever a second lunar month of Ashadha falls, the Nabakalebara is performed: entirely new images are carved and the old ones retired.
The process is specific. Parties of hereditary servitors search for daru, neem trees meeting a long list of marks. The new images are carved in a closed enclosure. Then, at midnight, in total darkness, a single blindfolded servitor with cloth-wrapped hands transfers the brahmapadartha, the life-substance, from the old image to the new. He does not see it and does not describe it afterwards. The old images are buried in the temple precinct.
The consequence is worth stating plainly: the images at Puri are not ancient objects. They are periodically remade, and the identity of the deity is held to survive the destruction of the thing it inhabited. Whatever is being venerated is explicitly not the wood.
The god who goes outside
The second practice cuts the other way. Once a year at the Rath Yatra, the deities leave the temple altogether and are drawn through Puri on three enormous chariots, built new each year from fresh timber and dismantled afterwards.
For those days the deities are in the street, and anyone at all may see them, including every category of person the temple excludes for the remaining year. The English word juggernaut comes from European accounts of these chariots.
The exclusion
Entry to the temple is refused to non-Hindus and foreigners, without exception and with no declaration available that would admit them. Jains, Sikhs and Buddhists are treated as inside the permitted category rather than outside it.
The rule is temple custom operating within a statutory administration, the managing committee is constituted under the Shri Jagannath Temple Act, 1955 and headed by the Gajapati Maharaja of Puri, rather than something the statute imposes. It has been argued over for decades, including in cases involving people of Indian descent refused at the gate, and it has not changed.
So the temple both excludes more strictly than almost any other major Hindu site and, once a year, deliberately puts its deities where the excluded can see them. Both facts are true and neither cancels the other.