Famous Irish People From The 60s

Before the Irish became "white" in the US, how were people able to distinguish them as "non-white?"

Scientific racists claimed the Irish were physically distinct from the English, supposedly more African and even ape like. See these illustrations from the time.  Obviously what was going on was stereotyping, caricaturing some features alleged to be common to Irish and not to English. The definition of racism I give to my students is- a system of ideology to justify inequality based on perceived physical differences. The differences are far more perceived than real. The people we currently call white are more typically pink in tone and sometimes, if Italian for example, can be darker than people we currently call Black. For example this actress is Black but does not fit the conception many people have of Black features.  If you haven't already, you may find the book How the Irish Became White of interest. And as another answer noted, much of the hatred directed at the Irish was for being Catholic.

How do British people see the Irish?

Depends where you are in Britain. People in England had a very strong hatred for Ireland but this has changed due to American influence. People in England like to copy what Americans do and since they have noticed that in popular culture Americans seem to like Ireland the people in England have followed suit. It's a weird thing really that England behaves like this, but then it does generally copy a lot of what America does. So whether this softening towards the Irish is real I don't know but it will curry favour with the Americans which England seems to want more than anything else.The Welsh I don't imagine have any ill feeling toward Ireland and probably feel a degree of sympathy to them. Wales is a conquered land and was annexed outright by England centuries ago. Indeed during the troubles the only place in Britain that the IRA bombed was England. No where else was hit but here.Scotland is very closely related to Ireland. The Scots are of Irish descent and are also Gaelic speakers. Culturaly, linguistically and historically Scotland and Ireland are very much similar up until the reformation where Scotland became largely Protestant and Ireland remained largely Catholic. But even during the troubles there was a great deal of support for Irish republicanism in Scotland. The IRA had arms depots in Scotland and built many of their bombs there. Even now you can see support for both sides all over a city like Glasgow with IRA and UVF spray painted on the walls. So there remains a Celtic brotherhood between Scotland and Ireland today.Northern Ireland i mother admittedly ignorant about but I would imagine this is where the strongest hatred for the Rep of Ireland is today. And it would be largely sectarian as the Protestant majority don't want to live under a catholic dominated government in the south. I might be wrong but he majority in the north of ireland do want to remain British.

Do Irish people get along better with people from Liverpool than they do with other people from the UK?

I don't know if that is true in all cases. But, there are strong ties and a closely shared history between Irish people and Scousers. Many surnames prevalent in Liverpool are Irish based. Plus, during the mass emigration of the Famine Years over 300,000 Irish people flooded towards the nearest city in England and the UK which happened to be Liverpool before moving onto other cities such as London and Glasgow. The Irish predominantly Roman Catholic weren't always welcomed with open arms of course as they gained a reputation for drunkenness and fighting. Whence, the famous sign sometimes seen in Landladies windows :“No blacks, no Irish and no dogs !”