Religious folk don't deny that the course of the moon can be calculated, some say that for establishing the start of the lunar month a sighting must be obtained, this is a complex issue that has nothing to do with believing or not in the predictable motions of astronomical objects.

With the moon sighting issue you presented this is similar in other countries too. However it isn't predominantly due to a distrust of science; sometimes certain scholars and groups will not adapt their rulings due to the fact that their parents and previous generations did this and they won't change not because they hate science.

The view in the UK on the moon-sighting debacle is that viewing the moon is necessary to commence the month as it was mentioned to the nearest meaning by the Prophet Muhammad (s.a.w) himself that we do not rely on calculations and the month is sometimes 29 and sometimes 30 (not 29 and a fraction of day as is the scientific view). The most correct and accepted view is that this isn't prohibiting or belittling astronomical calculations in deciding the month, rather it is a lessening of the burden to calculate and act upon exact calculations.

However the consensus is that astronomical calculations can be used to negate impossible viewings of the moon.

Things are complicated and the forces of history move in unpredictable and difficult to explain ways. We can identify broad trends which change cultures and societies: catastrophic events, economic changes, political changes, etc. But there's often no single explanation.