If quoted string is the only thing you need to handle extra (i.e. no escaped quotes, newlines, etc) and if you have GNU awk:

    $ echo '"foo","bar,baz"' | awk -v FPAT='"[^"]*"|[^,]*' '{print $1}'
    "foo"
    $ echo '"foo","bar,baz"' | awk -v FPAT='"[^"]*"|[^,]*' '{print $2}'
    "bar,baz"

For a more robust solution, see https://stackoverflow.com/q/45420535 or use other tools like https://github.com/BurntSushi/xsv