Every airplane in the United States has been certified for a maximum crosswind component (which is a calculation involving the direction of the wind and speed -- e.g., a 50 knot headwind 5 degrees off the nose will be less of a crosswind component that a 90 degree crosswind at 20 knots).

For a pilot to attempt a takeoff (or landing) when the crosswind component is known to be higher than the certificated maximum means the pilot is in violation of the plane's airworthiness certificate, would be subject to FAA action, has become a "test pilot," and is really stupid.

Each airline may well have its own procedures, though, that mandate no takeoffs or landings at crosswind components less than the certificated maximums.