Is it safe for insulation to be placed underneath existing knob and tube if only the insulation paper facing is touching the wires? Or is it be better to remove the insulation and leave a portion of the wall uninsulated? In WA, USA if that matters.
For the sake of argument assume replacing the K&T is not possible.
No, knob and tube wiring should not touch anything other than air, knobs and tubes. If you have enough access to add faced insulation, then you have enough access to replace the wiring.
In Washington it's completely OK to insulate directly over Knob & Tube wiring as long as it was first inspected, and a sign warning future workers of the hidden wires is placed.
Your question of "touching" insulation is the wrong question. Ask first what the breaker/fuse size is and what's the wire size. If you have a 20 amp breaker and the wire is 12 gauge you're all good for heat.
If you have a 20 amp breaker and the wire is undersized, then the issue of heat could in theory come up. Best bet is to reduce the breaker size.
Insulation batts should be split and placed on each side of the wires, with no airflow gaps left.
However I see water damage in that picture: that's got to be fixed regardless of your wiring. Insulating a section will reduce drying. That looks like a crawl space, not something you'd typically insulate.
