The simple answer is yes, airplanes can fly in the rain. Modern aircraft are designed to operate safely in a wide variety of conditions, including rain and snow. The most extreme example is the NOAA Hurricane Hunters, who fly right into some of the fiercest weather on the planet day in and day out.

Yes, it is perfectly safe for modern commercial aircraft to fly in rain. Airplanes are designed and tested to withstand extreme weather conditions, and rain itself has a negligible effect on the plane's ability to generate lift or maintain engine power. Jet engines are specifically engineered to "ingest" massive amounts of water without flaming out; during certification, they are subjected to tests where thousands of gallons of water are blasted into the intake. The primary concerns with rain are reduced visibility during takeoff and landing and the potential for slick runways, which pilots handle by using specialized braking systems and thrust reversers. If the rain is accompanied by severe thunderstorms, lighting, or extreme wind shear, a pilot may delay the flight or divert, but the "falling water" of a standard rainstorm is a routine occurrence that poses no threat to the structural integrity or safety of a flight.