There is certainly such a thing as homomorphic encryption (https://en.wikipedia.org/wiki/Homomorphic_encryption), which allows one to perform transformations on encrypted text without being able to decrypt it. As long as one of the transformations that can be performed is a measure of closeness (which is certainly the case for fully homomorphic encryption (https://en.wikipedia.org/wiki/Homomorphic_encryption#Fully_h... )), and as long as you know the ciphertext of the possible numerical responses, then you can read off closeness without being able to decrypt the hash.
The emphasised bit is a drawback, but it demonstrates the theoretical possibility; and, although I don't know of an implementation, nor do I see anything inherently contradictory about a (non-reversible) system designed intentionally to reveal closeness information.
There is certainly such a thing as homomorphic encryption (https://en.wikipedia.org/wiki/Homomorphic_encryption), which allows one to perform transformations on encrypted text without being able to decrypt it. As long as one of the transformations that can be performed is a measure of closeness (which is certainly the case for fully homomorphic encryption (https://en.wikipedia.org/wiki/Homomorphic_encryption#Fully_h... )), and as long as you know the ciphertext of the possible numerical responses, then you can read off closeness without being able to decrypt the hash.
The emphasised bit is a drawback, but it demonstrates the theoretical possibility; and, although I don't know of an implementation, nor do I see anything inherently contradictory about a (non-reversible) system designed intentionally to reveal closeness information.