Time does a lot of things, but in the parish setting anecdotal data tells me that the run-of-the-mill parish is more likely to remain insular than it is to choose to do things to make it more accessible to outsiders. It is the ambition of the parishioners that determines which route a given church will take. The soft phyletism of a parish that doesn’t announce its service times online (or in English), that performs those services almost entirely in another language, etc. has no methodology for taking in new members and few parishes have enough young children in attendance that they can replace their aging members as they pass on much less grow. Oddly, the same people who acknowledge they have something wonderful (e.g. the One, Holy, Catholic, and Apostolic Church) are also befuddled by visitors.
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The Beautiful Path 