Mix yogurt, 1 tablespoon lime juice, cumin, chipotle and 1/2 teaspoon salt. Coat chicken and refrigerate for 30 minutes; the marinating period is included in prep time.
Heat a 12-inch skillet over medium heat. Warm tortillas one at a time for about 20 seconds per side, stacking them under a clean towel as they finish.
Wipe the empty skillet with a paper towel, add 1 tablespoon oil and raise the heat to medium-high. Scrape excess marinade off chicken and cook cutlets in 2 batches for 3 to 4 minutes per side until each reaches 165°F; discard remaining raw marinade.
Transfer cooked chicken to a clean board to rest. Add remaining oil, poblano, red pepper, onion and remaining salt to the skillet and cook for 7 to 9 minutes until tender with browned edges.
Slice chicken across the grain into narrow strips. Return it with its juices and remaining lime juice to the peppers and toss over low heat for 1 minute.
Divide filling among the 8 warmed tortillas and serve 2 fajitas per portion.