Why do alternate web browsers want access to "Chrome Safe Storage" in my Keychain?
There's probably a couple of things going on here:


Vivaldi - In terms of Vivaldi this is something that's been happening for at least a couple of years, although it's not always triggered. You may want to read What is the Chrome Safe Storage discussion at Vivaldi's forums.
More generally - There seems to be an issue recently where a number of apps are requesting access to Chrome Safe Storage. It's not just happening with browsers, but other apps too. I first noticed this in mid-July on an iMac running a 3rd party video downloader/converter. I'm not sure what changed, but some of these app developers have had to issue updates to remove this behaviour.


In terms of the info that's stored there - it's basically a secure location to store credentials such as passwords for sites you visit. 

The advantages and disadvantages will differ depending on the app:


in the case of browsers it will mean things like having to manually log in to sites you want to visit. Obviously the benefit is not having to do this.
in the case of other apps (such as the video downloader/converter I mention above), the user whose iMac had this issue could only convert videos, but not download them. (Note: In their case an update fixed this).


Further reading 

The following may be of interest:


Google Chrome wants to use your confidential information stored in...your keychain
Bug 178358 - A pop up message "Google Chrome wants to use your confidential information stored in your keychain"