I'm not sure if it's been mentioned but the likes of Fairport Convention, Steeleye Span and others also included many Scottish and Irish tunes in their sets back in the day.

Also, Scottish and Irish bands would have included songs and tunes from each other's countries too. The Dubliners sang "Mormon Braes" for instance and The Bothy Band played "the Laird of Drumblair".
The JSD Band also played lots of tunes from Ireland and further beyond.

I think in recent years, traditional music has general become more ghettoised or, maybe, specialised (to use a less controversial term).
There now seems to be various groups, gatherings etc which like to focus on on certain genres in much more detail where as there used to be much more of a mixture and cross over. More "purist", I suppose, although the term has slightly different connations now and is not necessarily derogatory any more. There seems to be an exclusive project or gathering for just about every form of trad music in Edinburgh these days.

Yes, I do know that many of the younger bands still mix things up a bit, push the boundaries and so on but that's more a perfromance thing.