Mix buttermilk and Tabasco in a resealable plastic bag. Add chicken tenders and marinate for at least 1 hour or up to 1 day.
Preheat oven to 225°F. In a shallow dish, mix flour with salt and cayenne pepper. In a shallow bowl, beat together eggs with 2 Tbsp. water. Place bread crumbs in a separate shallow dish. Line a baking sheet with wax paper.
Remove chicken tenders from buttermilk, draining any excess, and dredge individually in flour mixture, shaking off excess; then dip into egg, draining any excess. Next, dip chicken in bread crumbs, pressing gently into crumbs to coat. Place on baking sheet. (Chicken may be prepared up to 5 hours ahead; cover and refrigerate.)
In a large skillet, heat 1/4 cup vegetable oil over medium-high heat. When hot, add one third of chicken tenders and cook, turning, until golden, about 4 minutes. Transfer to a baking sheet and keep warm. Wipe out pan and repeat cooking procedure in 2 more batches with remaining oil and tenders.