That’s called ‘barre’, and it’s a valid technique. Some lines can’t be played without it. So it’s a good thing to know. However, it’ also important to know the other options: rolling and using two fingers. So I’d say, keep practicing those too, so you’ll have options.
I’m not sure I understand this. When I play, for example, c-g on the G and D strings at the fifth fret using the rolling technique, my finger keeps contact with the G string when I fret D string. So the G string is muted in a very natural way.
When I use the rolling technique, I’ll often place my finger on both strings, but only push down one, so the other is muted. To change the notes, I press my finger down on the other string, but it still keeps contact with the first string I played. So it’s like a barre, except that only one string is fully pressed down at a time. This requires less force than a barre and it takes care of muting.
To try this, place your fingers as in the picture you posted. Now to play the D string, lift your finger a bit from the G string, so that the tip of your finger frets the D string and the flesh of your finger mutes the G string. Then, to play the G string, push down on the G string (that’s the rolling motion), while the tip of your finger keeps light contact with the D string, so it is muted.
