An obviously nifty idea by the Variations on Normal. It solves the problem of hygiene and the pesky paste that never completely squeezes out from the other side of the tube.
I suggest clearly color coding different sides of the tube, i.e. “my side is red and your side is blue”, etc. Still could lead to potential conflicts, as any sharing, because eventually one would have to squeeze at the back of the tube, effectively depleting your partners side of the paste. The cost and the environmental impact of the extra cap might not be economical in the end. But what a fresh idea!