Extra care is given to wind instruments simply because you use your mouth to play. Touching the mouthpiece with your lips means you should not let others play unless they bring their own, although, that is unlikely to happen. It is a personal instrument to prevent disease/virus from spreading, to or from, you.
Cleaning it regularly is another way to care for your instrument. Play with it regularly to prevent unnecessary collection of grime. Use trumpet valve oil when needed to avoid discoloration and rust buildup. Also, make sure you have the proper case to store your instrument. Giving proper care makes your instrument last longer.