Preheat the oven to 350 degrees F (175 degrees C).
Pour flour onto a work surface. Rinse pork tenderloins, pat dry, and then dredge in flour. Shake off excess flour and season with salt and pepper; some flour may remain.
Heat oil in a large skillet over medium heat. Add pork to the hot oil and cook until well-browned, 2 to 3 minutes per side. Transfer to a medium baking dish leaving any oil and drippings in the skillet.
Add onion to the pan drippings and cook over medium-low heat for 5 minutes. Add mushrooms and saute until onion is translucent and cooked, about 5 minutes. Pour the onion-mushroom mixture over the pork.
Whisk beer and soup mix together in a bowl until well blended. Pour beer mixture into the baking dish, making sure that it both covers and surrounds the pork, mushrooms, and onions. Cover tightly with aluminum foil.
Bake in the preheated oven until pork is slightly pink in the center and gravy is bubbling, about 1 hour. Remove from the oven and set aside, still covered, to allow it to cook a little bit longer outside of the oven, about 10 minutes longer. An instant-read thermometer inserted into the center should read at least 145 degrees F (63 degrees C).