Many guidebooks for travellers to Greece urge travellers to observe dress codes when visiting churches, chapels and monasteries, and though some women may balk at not being allowed into some of these places in trousers (even when they cover the entire leg), one can understand local chagrin in island villages where young girls in bikini tops and shorts have been seen to stride nonchalantly into churches, unaware that for the local people, such scanty attire represents a profound lack of respect.
Visitors are best advised to accept the topical dress codes in religious localities like churches and monasteries or to stay away.
Another area where respect for local custom is needed is in regard to mourning of the dead, with playing of music in small communities where someone has died deemed entirely inappropriate.
Though this may seem strange at first, if one considers that small communities in Greece consist mostly of several families that have intermarried over the generations, making the entire community one large extended family, it is understandable that all are affected by the death of one of its members, especially if relatively young.
So travellers staying in such communities might take mention of a death in the neighborhood as a signal to not sit on the veranda playing loud music or having highly audible parties, though one can always simply ask the proprietors of the place where one is staying what behavior is appropriate in the particular situation.