I just finished How the Irish Became White which was very interesting. According to the author the Irish joined, and then replaced free blacks at the bottom of the economic ladder and might have remained stuck there if America had developed a caste system rather than racism.
Lots interesting material in it about the politics & social mores of the time. One myth it disputes is that the Irish had an easier time assimilating because they already spoke English (a “fact” I always took for granted). According to the author, among the “famine Irish” as many as one-third spoke no English at all and many more only limited English.