In a large bowl, stir together the vinegar and water. Fold in the remaining ingredients and let sit for at least 24 hours.
In a blender, purée the ancho chile and chipotles in adobo sauce until smooth.
Heat the oil in a large pot. When hot, add the onions and garlic and sauté until soft.
Add the tomato purée and half of the chipotle purée and cook down for 5 minutes, stirring constantly.
Stir in the cremini mushrooms and cook until softened.
Add in the hominy and water and bring the soup to a boil. Season with salt and pepper.
Taste the soup for spiciness and add more chipotle purée until the soup has a nice spice to it without overpowering.
In a small bowl, combine the cilantro and queso fresco.
Divide the posole between bowls. Top with pickled vegetables, queso fresco and serve with tortilla chips.