The key here is context and the context is very clear that it's a positive thing rather than a negative.
"Up the Micks", "Fighting Micks", "Micks March", "Mounted Micks" and so on cannot be construed as being derogatory in the context they're used within the army.
It's no different to the examples of "Jock" and "Taff" above. If you think there aren't Irish and/or Northern Irish soldiers in the British Army who prefer to be known by "Mick", you'd be wrong.
You can ignore that if you want, but it doesn't change a thing.
Equally, there are plenty of people who get the context and understand it, so don't get offended.
For that reason, I quoted RTÉ as well to highlight that.
As for social media and internet in general, the problem there is a process called context collapse:
"Context collapse "generally occurs when a surfeit of different audiences occupy the same space, and a piece of information intended for one audience finds its way to another" with that new audience's reaction being uncharitable and highly negative for failing to understand the original context."
It's unfortunate and a sign of polarising of communities that some seem determined to ignore the literal, actual context in terms of the Irish Guards leading the Trooping The Colour yesterday.
Their role yesterday was a great honour. How likely do you think it is that anyone was being derogatory in referring to this regiment as "The Micks"? Their own nickname?!
That some took it out of context and, as a result, took offence does not correlate to literal offence here. That's their own problem as a result of context collapse and wanting to respond emotionally.
Most recruits to the Irish Guards from the island of Ireland are from Northern Ireland with most of these from the Protestant community. Of course, some are from the Republic of Ireland as well as from Great Britain. Indeed, some are not from the British Isles.
But all who join the Irish Guards are known as "The Micks".
The Irish Guards and other Irish formed regiments known as prefix "Micks" have no problem with it. It won't be going anywhere.