The name McCrie is certainly not amongst the most common, and its derivation is obscure. When it was first used is unknown. There is an IGI record of a Dr M'Crie in France, dated 1580, though the event, whether birth, death or marriage is not indicated. Neither is there any evidence that this name is related to McCrie, however the famous theologian Thomas McCrie was often documented as Thomas M'Crie, suggesting that the two are perhaps synonymous.
The International Genealogical Index for Scotland shows 168 entries for McCrie in Scotland. The earliest record for this surname is 1615 for Alexander McCrie in Dumfries.
There are 66 entries for McRie. The earliest entry is 1623, for Jonet McRie of Haddington, East Lothian.
Perhaps rather ironically, it appears now that there is noone bearing the name McCrie left in Scotland.
Because it is quite an uncommon name it is easy to assume that all or most McCries are related, though this is not the case.

The first appearance of the McCrie name in my direct line are the brothers James McCrie (b. 1799) and William McCrie (b. 1803). Interestingly, the younger siblings appear still to be McCrea or McCrae. Their father was John McCrae (b. 1768); his father William McCrea (b. 1736) and his father in turn, Heugh McCrea (b. abt 1700). I haven't been able to get further back than that yet.
On William McCrie's 1857 death certificate, his parents were listed as John McCrie and Elizabeth McCrie, perhaps suggesting it was John who took on the name McCrie from McCrae. Alternatively, it may just have been assumed at the time of writing the death certificate that the parents of William McCrie were also McCrie.

The question clearly is, what caused the change?

A simple answer is that it was an error, that there was no intention to have the name written 'McCrie'.