Sacred objects carry rules that outrank ordinary politeness, and the safest universal default is simple: do not touch unless invited. The specific patterns worth knowing: religious texts are handled with particular reverence in several traditions, kept elevated and clean and never placed on the floor, with some traditions restricting who may touch them at all. Statues and images of deities or revered figures are for viewing, not touching, climbing, or posing against, and turning your back on certain images for selfies causes offense at some sites, famously so in some Buddhist countries where disrespectful photos with sacred images have led to actual legal trouble for tourists. Altars, offerings, and ritual implements belong to the worship in progress, so walk around, not through, and never sample or move offerings. Feet are the recurring theme across Asia: pointing them at altars, statues, or people, or stepping over sacred items, reads as serious disrespect.
National flags sit in a parallel category, with desecration, and sometimes uses as casual as clothing or ground cover, being illegal in a number of countries.
The behavioral kit that keeps you safe everywhere: hands behind your back in sacred spaces as a habit, follow barriers and signage literally, watch what worshippers do and stay one step more conservative, ask before photographing anything on an altar, and accept a correction from custodians with an apology rather than debate. Reverent curiosity is welcomed in almost every tradition; casualness with the sacred is not.