Correctly hashed (with salt and a memory+time hard hash) passwords are taken to be brute-force hard to crack.
In that sense it's as safe to publish such hashed passwords on the internet, in the same way a website's public key is published on the internet. In fact, it's good practice to set hash parameters such that it's slower to brute-force passwords than asymmetric keys (e.g. TLS certs).
However, the big difference is that TLS private keys are randomly generated, and of a fixed length, whereas passwords are user chosen. So an attacker could do a dictionary attack and probably uncover a number of passwords using that (e.g. just try out "password" on all the hashed passwords). Hashed passwords are only as hard to crack as the passwords themselves.
In that sense it's as safe to publish such hashed passwords on the internet, in the same way a website's public key is published on the internet. In fact, it's good practice to set hash parameters such that it's slower to brute-force passwords than asymmetric keys (e.g. TLS certs).
However, the big difference is that TLS private keys are randomly generated, and of a fixed length, whereas passwords are user chosen. So an attacker could do a dictionary attack and probably uncover a number of passwords using that (e.g. just try out "password" on all the hashed passwords). Hashed passwords are only as hard to crack as the passwords themselves.