When you have great awe and respect for someone or something, and you show it by respectfully worshiping that person, thing, deity, or musical group, you are being reverent.
Originally, the word reverent was used only in religious contexts, but now it works when people are just acting like they’re in a religious setting (even if the object of their worship is a sports star or political pundit). People are occasionally reverent in regard to antique cars, supermodels, spelling bee champions and giant TV screens. Reverent is related to the verb revere, which is also about having or showing respect for someone or something.