What is Gnome Keyring / Seahorse and why it's storing my passwords in plaintext?
What is Gnome Keyring
It's a password storage system – exactly like the one inside Chrome, and exactly like the one inside Firefox, except it's system-wide and it's encrypted by default.
This is in fact why Chrome uses it – Chrome's own password storage is not encrypted. GNOME Keyring is a system component, knows your login password, and can use it as the encryption key for everything else. Chrome is just an app and doesn't have any keys it could use.
In KDE, Chrome uses KWallet for the same purpose. (On Windows, I think it has its own database, but asks the OS to hold just the "master key".)
What about Firefox? Well, technically Firefox's password database is encrypted. However, the encryption key is stored in a file right next to the database meaning other programs can easily decrypt the passwords anyway. Without a system keyring, password storage is like writing the PIN code on your credit card.
Seahorse?
Seahorse is the management app for GNOME Keyring.
Why it's storing passwords in plain text,
It's not. On disk they are encrypted (using your Linux password). Of course they must be decrypted in memory, so that programs could use them. Chrome can't autofill a password unless it can access that password in plaintext.
(Note again that GNOME Keyring encrypts its password storage, but Chrome itself does not.)
allowing anyone to see passwords?
Do you give your Linux password to anyone? If not, then anyone cannot see the keyring contents without your login password.
How can I disable this from my computer?
You can start Chromium with the --password-store=basic option. Note that with this option you would lose any encryption you had. The passwords would be stored in a SQLite3 database ~/.config/chromium/Default/Login Data, in plain text.
The most interesting question: why it's storing passwords without my consent?
You gave your consent when Chrome asked "Do you want to save this password?" and you clicked "Save" in the popup. Whether the password is hidden inside Chrome's own database or a common system one is irrelevant.