It seems a modicum of regulatory creativity would result in a marvelous new invention: a bike lane that is open to parking on Sunday mornings. This would inconvenience approximately zero cyclists, since Sunday morning is a time of low traffic.
That is exactly what was done in Philadelphia on Pine and Spruce streets. These are East-West bike lane "arterials" that allow parking on Sundays.
Except for people who ride a bike to church.
As observed above, they will face very little traffic, because most commuters are godless heathens who are snug in their beds on Sunday morning. There is nothing wrong with travelling by bicycle in the street in general, but certainly even less wrong with doing so near a church on Sunday morning. Bike lanes with no nearby churches wouldn't have this special rule.