For SHA-2, SHA-3, Skein, Blake2, etc. the password is the weakest link in the chain. There are two potential attacks on such hashes which allow user impersonation. Besides things like rubber-hose attacks, surveillance, and social engineering.
- Determine the password by brute force, guess-and-check
- Search for another "password" which produces identical output
The difficulty of method one depends on how random the password is. If you use an RNG appropriate for generating cryptographic keys, read 128 bits, then use base-64 encoding to make the password human-readable, then this attack would be totally infeasible.
(Normally you'd use something like Argon2 to hash passwords. Humans fail to generate good passwords, so a hash function which is slow and costly to parallelize should be used instead of one of the algorithms listed a the start of this answer. But a fast, cheap cryptographic hash would suffice if all passwords are as difficult to guess as, say, an AES key.)
Method 2 is ineffective for the algorithms mentioned above. They are all believed to have at least 256-bit preimage resistance. That means there is no search procedure faster than bruteforce that can produce some message which hashes to a given output. Such a search is expected to take as much work as evaluating a hash function 2255 times.
(Argon2 has as much preimage resistance as Blake2. So it should still be favored over cheaper hash algorithms for weak passwords, especially human generated ones. Argon2 has preimage resistance by design, as is intended to be used for hashing passwords.)
In summary, revealing password hashes is safe if all passwords are known to be exceptionally strong and the hash algorithm chosen is preimage resistance. Otherwise hashes revealed to the public are vulnerable.
"Exceptionally strong" implies that the passwords will be longer and likely more difficult to memorize than typical passwords.