Ya I dont play acoustic styles, but i do know what you mean. Since im not usually using the open strings when i do like full neck tapping runs i can get away with a sweat band for a mute, but for you id say just use less of your finger when tapping because it runs less of a risk of hitting unwanted notes.
Also just practice what you are playing more, and you should only hit the notes you want. Way easier said than done but its possible.
