Did the black and tans win medals down in Flanders? Did they have a wife to tell how they slew them arabs two by two? Did they fight in the middle east? Did the IRA make them run like hell away?
As unrest in Ireland heated up in 1919 and 1920, the Royal Irish Constabulary (the main police force in Ireland) faced some significant problems. British rule was becoming increasingly unpopular, and the RIC was coming under attack from groups fighting for independence, most notably the Irish Republican Army. The IRA viewed the RIC as one of the prime symbols of the British power in Ireland, and actively targeted RIC members. The RIC was driven out of many rural areas, and members were often denied service or actively harassed when out and about. These factors all led to a lot of Irish members of the RIC resigning, either out of personal conviction, pressure, or fear.
To shore up the numbers and try to quell the unrest in Ireland, the British government decided on a strong recruitment campaign of new members into the RIC. This campaign focused on the thousands of men who had recently returned from World War One, many of whom were unemployed. Posters promised that "if you are an ex-service man YOU CAN JOIN THE RIC TODAY," along with fairly high pay and a month's paid leave every year. Since they were recruited and trained in a relatively short period of time, there weren't enough official RIC uniforms for everyone. Instead, the new guys got khaki army pants and a dark top, which ended up being the basis for their nickname, the "Black and Tans."
There are a few things to get straight about the song "Come Out Ye Black and Tans." First off, it's not necessarily sung to a group of Black and Tans under the strict definition of the term. Instead, the singer tells us that he lives in a Protestant/Unionist neighborhood of Dublin, or at least one "where the Royal drums did beat," and that his drunken father would shout the threats and taunts at his neighbors. Fife and drum bands were and remain a popular symbol of Loyalist culture in Ireland, so the line about "drums" is likely referring to those bands marching through the neighborhood.
This is an important point to make, because the vast majority of Black and Tans were not from Ireland, so the chance that any of the singer's neighbors in Dublin were actually members wasn't particularly high. Of the ~10,000 men recruited into the Black and Tans, less than 1,000 were born in Ireland. It's also worth noting that while the RIC was the main police force on the island, Dublin had its own police force, the Dublin Metropolitan Police. The DMP were not only unarmed, they were also on the whole more sympathetic to the Irish nationalist cause, and did not play nearly as large a role in the fighting. The IRA mainly targeted a single division which focused on plainclothes detective work, leaving the uniformed officers to patrol their beats in (relative to the RIC, at least) peace. In fact, most Black and Tans weren't stationed in Dublin at all, as they were sent to areas where the IRA was strongest, mostly in Munster and Connacht.
Instead of being used literally, the term "Black and Tans" in the song is being as used as a broader epithet against those who collaborate with or support British rule on the island of Ireland. This usage has continued, and you're liable to get called a "Tan" even today by some if you seem to have unionist or pro-British sentiments. So, rather than being a call to arms against a group of actual Black and Tans, the song is an invitation to a drunken street-fight, extended by a Republican Irishman to his Unionist neighbors.
As for the accuracy of the text, let's start with the chorus. It is entirely plausible that some of the singer's Dublin neighbors had won medals while fighting in Flanders, as over 200,000 Irishmen served in the British armed forces during WWI. Since the actual Black and Tans were ex-servicemen themselves, many of them also would have fought in Flanders. Moving on, the IRA specifically targeted small RIC barracks in rural areas, forcing them to flee many towns including the town of Killashandra in County Cavan. The lanes of Killashandra are, like most lanes in rural Ireland, quite green, although whether they can accurately be described as "lovely" is a matter for locals to decide. So far, so good on accuracy, although again it should be stressed that the likelihood that any Dublin neighbors were involved in Killashandra specifically is low. The town itself was likely picked as a "close-enough" rhyme for "Flanders," and did not play a large role in the Irish War of Independence.
The line in the second verse about "how you slandered great Parnell" is a reference to Charles Parnell, the most powerful Irish nationalist politician of the late 19th century. As a prominent MP and leader in the push for Home Rule in Ireland, Parnell had a few incidents in which he could have been said to have been "slandered." The line is likely referring to a set of letters published by The Times of London in 1887 that encouraged violence and sympathized with the killing of the Chief Secretary of Ireland and his under-secretary in 1882. These letters were purportedly written by Parnell, but were later exposed as forgeries. Parnell also spent some time in jail after opposing the Land Act of 1881, and a long-standing affair with a married woman was exposed in 1890. All of these may have hurt his standing with some and invited slander, but he was still revered as a hero in Ireland, especially after his untimely death in 1891 at the age of 45.
The "heroes of sixteen" referred to in the second verse were those who fought in the 1916 Easter Rising. It was not an altogether popular uprising in Ireland, and sentiment was mixed at best even among those who were looking for independence. However, the quick executions of the leaders, including tying the mortally wounded James Connolly to a chair to shoot him, were wildly unpopular. The reaction to those executions is credited with starting the chain reaction that led to the push for independence in Ireland a few years later.
The third verse mocks some of Britain's colonial "achievements," including the Anglo-Zulu War and the British occupation of Palestine. This draws a direct parallel between the actions and excesses of the British Army in far-flung places against lesser-equipped opponents and the actions of the RIC in Ireland. This sets the British up as the powerhouse, and implies that the Irish are not just fighting for their own independence, but against the enemy of a much larger group of people.
The fourth verse contains one of the most pertinent pieces of information in regards to the song, although it's often missed by those who don't know their Irish folk music history. The singer says that one day his kids will sing a "verse or two of Steven Behan's chorus," implying that Stephen Behan is the father in the song. "Come Out You Black and Tans" was written by Dominic Behan, a noted writer and member of one of Ireland's well-known literary and Irish republican families. Dominic was born in 1928, so he did not witness the War of Independence or the actions of the actual Black and Tans. Instead, this is a reminder that the term is being used more broadly to refer to any potential pro-British sentiment, especially in Northern Ireland, which remains part of the UK. The song was not written in the heat of the moment against the Black and Tans, it is a rallying cry for what Irish Republicans see as the fight against the continuation of British oppression in the North, as well as a reminder of Ireland's history, seen through a Republican lens.