Yes, and it is one of the most appreciated forms of respect a visitor can show. Periods like Ramadan in Muslim countries, Holy Week in strongly Catholic ones, and major temple festivals in Hindu and Buddhist regions change the public mood noticeably.
Around sacred processions and ceremonies, the etiquette is consistent worldwide: dress conservatively with shoulders and knees covered, keep your voice down, do not cut through a procession or block it for photos, and put the camera away if worshippers seem uncomfortable. Alcohol sales are sometimes suspended on major religious days, and nightlife may pause entirely, which surprises some visitors.
None of this diminishes a trip; religious festivals are often the most memorable thing you will witness. Check the dates for your destination since most move annually with lunar calendars, and read a short etiquette guide for that specific festival. Locals notice respectful visitors and often respond by welcoming them right into the celebration.