Burray on Wikipedia.
 

Burray Village, St. Lawrence. ND 4719 9567. © Martin Briscoe. This source, which says it is now former dates it to 1856, originally as United Presbyterian, closing "just after" 1969.

Kirk Taing, the Old Parish Church (also dedicated to St. Lawrence). ND 4917 9643. © Martin Briscoe. Category B listed.

Overfaulds - the 2022 Streetview of the long-closed Church (or building on its site), shown on maps from the late 19th and early 20th centuries, near the south end of Echna Loch. None of the maps identify it any more closely. ND 4732 9363. A map of 1882 shows a Baptist Chapel just to the east of Echna Loch at ND 4784 9661. This source has dates for a Baptist Church on the island (and I can't find evidence for another) for 1802-1952. 2022 Streetview.

As far as I can tell, there aren't any other places of worship on the island, either past or present - unless you know better!