Place red onions in a medium bowl and add white wine vinegar, sugar, 2 teaspoons salt. Massage onions with your fingers until they begin to break down and vinegar turns pink. Set aside. This can be done several hours in advance, or up to a day in advance; keep covered in the refrigerator.
Heat a large nonstick skillet over medium-high heat. Add chickpeas and baking soda and heat, stirring continuously, until chickpeas are warmed through and mixture begins to sizzle on the edges, about 3 minutes. Continue to cook, stirring, for 2 more minutes.
Transfer chickpeas to a large bowl, fill with cold water, and rinse and drain 4 to 5 times, gently rubbing the chickpeas between your hands to loosen the skins. When draining, use a small skimmer to discard skins, or pour off the skins from the top of the bowl before refilling with fresh water. Repeat until the water runs clear and no skins remain.
Transfer chickpeas to a food processor. Add tahini, garlic, lemon juice, and salt to taste. Process to form a thick, chunky paste. Add 1/4 cup ice water and continue running processing for an additional 4-5 minutes. Add ice water by the tablespoon until mixture is velvety and entirely smooth. Season to taste with salt and additional lemon juice. Set aside.
Heat a large skillet over high heat. Add olive oil, swirl to coat, and add mushrooms and thyme. Season generously with salt and pepper and saute, stirring occasionally, until mushrooms are softened and deeply golden, about 8-10 minutes. Remove from heat and keep warm until ready to serve.
Spread hummus in a thick layer on a serving plate. Scatter with sauteed mushrooms and pickled red onions. Dress with a generous pour of olive oil and chopped dill. Serve with crudites and pita on the side.