Just my own experience...in our local area, Dublin 7, there is an Educate Together school that seems almost overwhelmingly white, irish, middleclass and lapsed catholic. Our local catholic national schools on the other hand have all classes, lots of faiths, lots of nationalities, lots of various ability levels and seem much more mixed. I understand that some people don't like the idea of religious doctrine being taught in school and that's fine but I don't think people should fool themselves into thinking that the ET route is more integrated. If anything, the fact that the kids name needs to be down so far in advance mitigates against immigrants, migrants and just generally against the people that haven't put a huge amount of thought into it.
Also, anecdotally, the ET primary school children don't seem to end up in our local secondary schools - almost all that I know of have plans for fee paying secondary school. I think ET has an elitist whiff off it.