Yes, commercial aircraft are designed to operate safely in heavy rain, but wind is subject to much stricter operational limits. Rain itself is rarely a problem for modern jet engines, which are tested to "ingest" massive amounts of water without flaming out. The primary concern with rain is visibility; if the pilots cannot see the runway lights clearly, the airport will initiate Low Visibility Procedures (LVPs), which may slow down operations. Wind, however, is a different story. Every aircraft has a maximum "crosswind component"—a limit on how much wind can be blowing sideways across the runway before it becomes unsafe to maintain directional control. If the wind is blowing directly down the runway (a headwind), it actually helps the plane take off faster. If there is a severe thunderstorm, the main danger isn't the rain or wind itself, but wind shear (sudden changes in wind speed/direction), which can cause a dangerous loss of lift. In such cases, pilots will wait for the storm cell to pass.