Turn on a multi-functional pressure cooker (such as Instant Pot) and select Sauté function. Add olive oil to the pot. Cook and stir onion and guajillo chiles in hot oil for 3 minutes. Add garlic, cumin, and oregano; cook for 2 minutes. Cancel Sauté function.
Pour broth, pinto beans, hominy, and enchilada sauce into the pot; stir to combine. Close and lock the lid. Select high pressure according to manufacturer's instructions; set the timer for 20 minutes. Allow 20 minutes for the pressure to build.
Release pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Unlock and remove the lid. Discard guajillo chiles. Stir in cilantro and lime juice.
