@Sarah3744 Under non-pandemic circumstances that would be an unusual service for police to perform; it seems unlikely that they would be doing it unless they were required to. Have you checked what the current restrictions on tourism in your destination are? Are you sure everyone in your group is legally permitted to stay overnight there?
You always have the right to cancel, but being uncomfortable with the registration process wouldn't qualify you for an exemption from the host's cancellation/refund policy, so you might lose money on that. Just the same, an airline won't refund your plane ticket just because you find the questioning at passport control too invasive.