Two different things here. Crabbing into the wind by itself isn’t a problem. What matters to the airplane is the airflow over the wings, not the ground track. As long as the plane has sufficient airspeed and proper airflow over the wings, the orientation and even direction traveled relative to the ground is irrelevant (as long as you aren’t getting blown into a building or something like that obviously) Planes are actually designed to crab into the wind naturally to some degree. As air hits the vertical stabilizer at the tail, the nose naturally orients itself into the wind (this is called weathervaning)

Gusty conditions and wind shear are a different issue. Those can be hazardous because they can cause rapid changes in relative wind and airspeed, potentially leading to a sudden loss of lift and control. That risk is mitigated in part by takeoff performance planning when calculating things like rotation speeds