What hat do you wear with a kilt?

[MacSpadger]

I don't generally wear hats much, but I do sometimes wear a caubeen. Technically any hat is a caubeen, but it's usually taken to mean the Irish equivalent of the balmoral, with no toorie (bobble) unless you are in the Canadian army(!), and worn raked to one side. Scottish balmorals always come with a toorie, and only Americans wear a balmoral raked, Scots wear them flat like a pancake! Obviously, caubeens and balmorals have a common origin in hats worn by the Gaels who came to Scotland from Ireland, albeit they didn't wear kilts at that point.

Tams are the knitted version of a balmoral, and there is an Irish name for that type of hat, but seldom any call to use it!

The glengarry is basically the highland regiments' version of a British army forage cap. The Irish military even wear them, and so do pipers the world over, but if they have a military or uniform association it's not accidental.

As for diced bands on hats, the Irish view, correct or not, and obviously with the exception of Northern loyalists, is that it represents the crown, which is the British term for the British government. Pipe bands in the Republic of Ireland seem to have switched from green caubeens to black glengarries over time, but with a notable complete absence of diced bands. I don't think Scots take that view, even if they are pro independence. Evidently at least some Scottish Americans do.

I don't know where to begin here. Although it's become the norm for Scottish balmorals to have toories, historically most of them didn't and today not all of them do. As for, "only Americans wear a balmoral raked, Scots wear them flat like a pancake", have you ever been to Scotland and seen the variety of ways in which the balmoral is worn? Some guys wear them so "raked" that you wonder if they are glued to their heids in order to stop them falling off as they are jist aboot worn sideways.
As for the "caubeens and balmorals have a common origin in hats worn by the Gaels who came to Scotland from Ireland", I think you'll find that the origin of this type of headgear is the simple European bonnet from which the French beret, etc, also derives. It was worn throughout Europe in the 15th century. The bonnet seems to have travelled up through the low countries and reached the Lowlands of Scotland first, (where it was a staple headgear for hundreds of years). Although it may be seen as particularly Highland nowadays, even in the 1700's it was worn by Highlander and Lowlander alike. The origin of the Irish Caubeen (as we know it nowadays) is attributed to Owen Roe O'Neill around the 1610's. He is noted as having entered negotiations with the MacDonalds of Antrim, who had arrived from Scotland to claim title and territory. One story says that he had a bigger version of MacDonald's balmoral made to "intimidate him" by wearing a larger hat to the next meeting. The Royal Irish Rangers website says the Caubeen was adopted by O'Neill through association with the Highland MacDonalds of Co Antrim. Most sources seem to agree that the origin of the caubeen in Ireland is Owen Roe O'Neill around 1610 and that it was modelled off/adapted from the MacDonald headgear. Nothing to do with Gaels coming to Scotland, (and even that legend has been discredited many times).
Tam's are not knitted versions of the balmoral. Earlier bonnets/balmorals were also knitted. The name Tam also means the bonnet/balmoral and is an abbreviation of Tam O'Shanter, which is just another nickname for the bonnet/balmoral/boinead biorach, that came in the 19th century after the Burn's poem. The actual name Balmoral is itself a Victorianism, named after the Queen's place of residence. The bonnet, Tam and Balmoral were different names for the same thing. In 1915 a khaki style of balmoral bonnet was made for WW1 Scottish troops and this was named the 'Bonnet, Tam o' Shanter' which nowadays everyone calls the 'ToS'.
There is no way in which diced headbands represent any kind of allegiance to anything, they are simple decoration. I have only heard this mistaken view from the USA, along with the equally mistaken one that says the dicing means wounded in action. I have lived and worked on both sides of the Irish border and I have many long term friends in the pipe band world, it's just considered absolutely daft by those I have spoken to, uninformed nonsense. (BTW, the British Term for the British Government is just the Government). I don't see what diced headbands have to do with Scots independence either. Dicing doesn't appear in portraits or illustrations until after the mid 1770's, which is the exact same time that the Highland Society of London was formed and started having a massive say in what was considered Highland clothing, so there may be a connection there.