If I think back 30 years, or so, ago there was a fair amount of disrespect for our Irish neighbours around (eg. 'Irish jokes' etc.). Thankfully, a lot of that seems to have died out. The reasons for this are probably quite complex, but I would suggest such things as the emergence of Ireland as successful European nation and a more positive portrayal of Irish people in the British mass media have all helped.
Personally, I grew up listening to Irish traditional singers and musicians (as well as English and Scottish ones)- they convinced me (if I needed convincing) that Irish people and Irish culture have always been worthy of the highest respect.