It varied very much by time or place. As a cutoff point, I may as well begin with Wolfe Tone. For all that he was an anti-colonial revolutionary who fought for non-sectarian ideals despite his own Anglicanism, he was very much affected by the death of his cousin, James Wolfe, on the fields of Abraham in the name of the Empire. In the early 1790s, he attempted to join the East India Company but his application was slightly late, and he also proposed to Prime Minister Pitt a plan to establish a military colony on Hawaii. This was refused, and instead Wolfe Tone was drawn into Irish nationalist politics and the Society of United Irishmen. As reform within the system seemed totally impossible, it and he radicalized, and he went on to lead the Irish Rebellion of 1798, where he was captured and committed suicide before he could be hung; his final speech inspired Irish nationalists for generations evermore.

The next great Irish revolutionary moment was led by the pacifist Irish nationalist Daniel O'Connell. He initially led the movement for the repeal of the anti-Catholic Penal Laws, and after it was achieved in 1829 he fought for the repeal of the Acts of Union between Ireland and Britain, an effort which failed; he died in 1847, where his last speech in Parliament consisted of him begging Parliament to provide any aid to the Irish people, and he went so far as to declare he would accept the restoration of the Penal Laws in return for famine relief, but alas it was all in vain. In his career, O'Connell was extremely sympathetic to other colonized peoples, and he even declared himself the "Advocate of Humanity". He took part in the British movement against slavery, advocated Jewish rights, and even denounced the fate of the Australian Aborigines and the Maori. He also advocated Indian colonial reform, comparing colonialism in India to colonialism in Ireland, declaring,

There is [a] strange coincidence between the history of India and the sad story of Ireland. The subjugation of the former was only the enactment on a broader scale of the system of rapacity and deception by which the latter was subjugated. The support given by the English to the weaker O’Donnell in order to put down his more formidable competitor O’Neill, has been one thousand times imitated in India.

as well as

It is not alone the slavery of two millions of human beings, but of the hundred millions of human beings who now suffer the degrading slavery of having no title to their land – no right to their houses – no species of permanent property – because the maladministration of the British Government in India has left them beggars in their native land. When the last despatches came away people were perishing, by the hundred of thousands, by famine; streams were polluted with their carcases; the air was infected by corruption; famine stalked through a land which, but for tyranny and misrule, would be fertile and abundant.

It is a striking piece of colonial solidarity. He also advocated colonial reform, though I doubt his advocated reforms would have been enough.

But where his declarations of colonial solidarity were far more intense were American slavery. He believed it a total and utter abomination and spearheaded the World Anti-Slavery Convention where he met up with William Lloyd Garrison. He declared the United States an unholy union of slavery and republicanism and declared he would only visit it if slavery were abolished. He notably launched harsh invective towards the American Ambassador to the UK, Andrew Stevenson, declaring:

It is asserted that their very ambassador is a slave breeder, one of those beings who rear and breed up slaves for the purpose of traffic. Is it possible that America would send a man who traffics in blood?

It is a very intense criticism that caused Stevenson to ask for a duel for his satisfaction; ever the pacifist revolutionary, O'Connell said no, despite the honour codes of the era. In 1839, Henry Clay in the American Senate condemned O'Connell's intense anti-slavery remarks, and the British establishment believed it to be an obstacle to good relations.

Notably, Frederick Douglass visited Ireland, where O'Connell trumpeted him as the "Black O'Connell" for his eloquence.

However, in the 1840s, with the rise of a new generation of Irish revolutionaries known as Young Ireland who tended towards romanticism rather than O'Connell's late enlightenment nationalism, they believed O'Connell's anti-slavery views were a liability that stopped a flow of money from Irish-Americans (and they did, as they caused many splits of Irish nationalist societies in the US). Many of them regarded the "white slavery" of the Irish to be worse than the "black slavery" of Black Americans. It was revealing, that not all of the Irish nationalist movement agreed with O'Connell's statements of solidarity. These disagreements between "Young Ireland" and "Old Ireland" increased, and after O'Connell's death "Old Ireland" began to break apart. When the Great Irish Famine hit, it essentially stopped all Irish politics, and the Young Irish launched a rebellion in 1848 that failed badly when the Irish people were too hungry to take up arms. And though O'Connell's words were used to marshal Irish-Americans to the Union cause during the American Civil War, and though Indian nationalists found him inspiring, this moment of cross-colonial solidarity would never be met ever again. Though a whisper of O'Connell's solidarity with black Americans would be repeated when Bernadette Devlin's statements of solidarity with Black Panthers, and of course most notably John Hume's pacifist nationalist movement being heavily inspired by the American civil rights movement.

The Irish nationalist movement gradually rebuilt as the scars of the Famine slowly reduced. The Home Rule League, first under the moderate Isaac Butt and second under the more radical Charles Stewart Parnell, tended to be much more pro-empire than O'Connellism. It sought to wrap the Irish people into the creation of imperial whiteness and through that gain the Irish people their rights. It was a process that necessitated minimizing colonial solidarity, and notably the infamous white supremacist Cecil Rhodes gave Irish nationalists a large donation as he thought Home Rule would be a stepping step to a white supremacist Imperial Federation. But it still existed. Many Irish nationalists fought on the side of the Union in the American Civil War in the name of anti-slavery and republicanism, most notably Thomas Francis Meagher, and depending on which measure you use they were the largest or second-largest ethnic group (after Germans) in the Union Army. Fenians fought on the side of the Boers during the South African War, which is not really solidarity with the black South Africans of course but rather a solidarity with the Afrikaners, against British imperialism. It's another demonstration of questionable attitudes, and at the same time Parnellites fought for the British. Few at the time probably cared much of the Zulu.