As I understand it, 'muir' is the Scots form of the modern English 'moor'. According to the Oxford English Dictionary, both derive from the Old English 'mor.' That makes sense if I am right in believing that, more generally, (Lowland) Scots is largely derived from a Northumbrian form of Old English (Anglo-Saxon); this is a result of the settlement of much of southern Scotland (including Ayrshire) by Northumbrian speakers in the early middle ages.
So I would suggest that even if the Muir family are of Gaelic origin, they must at some stage have adopted a Scots (i.e. non-Gaelic) surname.