A solution that worked for me was starting Vivaldi in the terminal with vivaldi-stable --no-sandbox (as stated in this post). Although I haven't tested it extensively, and also haven't tested this with Chrome, I can confirm that browsing in Vivaldi works just fine now. I hope this works for you too.
Edit: to make it stick, you can edit the vivaldi-stable.desktop file in /usr/share/applications. To do so:
Open a terminal, navigate to the directory, enter sudo cp vivaldi-stable.desktop vivaldi-stable.desktop_backup (to make a backup - just in case something goes wrong), then enter sudo gedit vivaldi-stable.desktop. Once opened, look for the line starting with "Exec". It should look like this:
Exec=/usr/bin/vivaldi-stable %U
Change it to:
Exec=/usr/bin/vivaldi-stable --no-sandbox %U
Now you should be able to start Vivaldi, add it to your favourites (so the icon is always visible on the launcher) and open it from there the next time. It will save you the hassle of launching from the terminal.
There is also the option to change the Exec line in the section "[Desktop Action new-private-window]", but that is up to you.
Hope this helps!