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.