Margaret Orr born Londonderry she married John white in glasgow1843, her husband John also born Ireland, her mother Margaret Orr also her maiden name and her father Andrew Orr, her maternal grandmother Elizabeth Wilson and her maternal grandfather James orr, her paternal grandparents Andrew Orr and Mary Mcdowel.
Her husband John White his parents John white and Catherine Fairlie.
All born Ireland I suspect NI and as far as I know all Protestant.
What is your source for the parents & grandparents of Margaret Orr who married John White in 1843?
PRONI have an Orr family tree (D1717/2) and Dr. Mullin expanded on this in his book Aghadowey A Parish and its Linen Industry (1972). An Andrew Orr of Keely (Aghadowey Parish) & Millburn (Coleraine) (1786-1864), son of William Orr & Miss Molyneux, married Mary Holmes of Belfast. Their son Andrew Orr (1829-1870) married Lucy Erskine Acworth.
None of the information in the tree fits with any of the details you've posted but will include more so that you don't start tracing the wrong family.
Andrew Orr (1821 Coleraine?-1908 Australia), poet-
http://www.hidden-gems.eu/derry-orr.pdf dates given as (1822 near Coleraine-1895 Ballarat, Australia) here-
http://www.newulsterbiography.co.uk/index.php/home/viewPerson/1371Andrew Orr of Millburn, Coleraine listed in 1849 Dublin Almanac. There are likely many other references online.
There were Orrs in Derry (city), including an Andrew at a later date than your post indicated-
https://www.londonderrysentinel.co.uk/news/maiden-city-great-war-roll-of-honour-part-26-1-7315406Orrs of Co. Londonderry also in this thread-
https://www.rootschat.com/forum/index.php?topic=154826.0As you can see, it wasn't that uncommon a surname and they certainly weren't all Church of Ireland but in order to see if any church records do survive you'll need a more exact idea of location and dates.
Not sure if this is the same Andrew Orr & wife Margaret since they also haven't given any indication of dates or location-
https://www.ancestry.co.uk/boards/thread.aspx?mv=flat&m=3545&p=surnames.orr