Copyright can be CLAIMED on traditional material, as was apparently done by a "well known Irish family" (and also by Bob Dylan, though he did make changes)

If you don't agree, and want to use it yourself, your best strategy is to use a version which clearly predates the claimed copyright.

So instead of Wild Mountain Thyme/Will ye go lassie, you could sing Braes o' Balquidder. Not quite the same, but MUCH older (1797. I think)