This is a long thread!

From the ethnic Irish point of view, the only examples I have to go on are pictures of pipe bands in the Republic of Ireland, and what I see is that they either wear caubeens (usually dark green) or increasingly glengarries (usually black) with the kilt. They never wear a diced hat band, because they associate it with the British Army, and out of respect I would never do that either, even though I am actually British, having been born in England. They also never wear balmorals or tams, which makes sense as the caubeen is the Irish equivalent.

I have a green caubeen, although I am not really a hat person and usually prefer to be bare-headed anyway. The glengarry doesn't appeal to me atall, personally, although I have nothing against others wearing them. The same goes for flat caps, although my uncle and my son wear them, but they don't wear the kilt anyway.

Personally, I think adding the caubeen on my head weirds people out far more than the kilt, so I'd rather not wear a hat atall unless I really want to feel overdressed.

One strange anomaly I discovered on eBay is that light green caubeens with a dark green toorie were issued to Canadian Irish soldiers. Doesn't the toorie make it a balmoral? I suppose you have to be Canadian to understand!

Mind you, the caubeens issued to pipers in the Irish National Army are apparently officially designated as glengarries, which is even odder.