Pare the spines from the cactus, trim away the base and around the edges. Chop into ¾ -inch by ¼-inch pieces. Blanch in boiling water until tender. Drain and rinse thoroughly.
Trim bottoms from mushrooms and discard. Slice mushrooms. Combine the next 6 ingredients and toss with cactus and mushrooms. Marinate 4 hours, tossing occasionally. Drain off half of the marinade. Add the next 5 ingredients. Continue to marinate.
To serve, spoon some of the mixture into a warm tortilla. Top with tomato and feta.