Some East Lothian opens are run by the Artisan sections like the Bass Rock GC @ North Berwick which runs the Esmond Trophy and the Haldane Cup run by Dirleton Castle GC at Gullane. Both of these are historically restricted to members of East Lothian clubs so are not 'open' opens. The Ladies Cup (a gents comp - go figure ) is an open knockout at Gullane Nr 1, as many rounds as you can survive for £12 - best value in golf perhaps.
I'm playing in one at Manchester GC on Friday and the wording on the entry form states "The Competition is open to bona fide male members of recognised Golf Clubs."
However, I imagine this was written up before the iGolf scheme went live so it will perhaps change next year.
I don't know where I stand on it to be honest. I've a couple of mates who would love to be able to play in the occasional Open but are currently unable to because they aren't members of a club. Yet it makes no sense for them to join one as they work away all week and wouldn't get the benefit of a membership.