Why?

It ended up that way with religion as a defining feature, although it started as more of a territorial and political thing.

Israel vs Muslim? Are you thinking of Israel vs Palestine?

Ireland is an occupied country by the English. With Southern Ireland independent, the Irish wish to unite the North back with Ireland. But the British have colonized and been living in the North that do not want the union with Ireland, they are of course loyal to the English and the crown. There has been centuries of discrimination against the Irish in the UK, even in their own land, Ireland. These Irish happen to be Catholics while the British are Protestants. So the discrimination is extended to Catholics and Catholicism. If an Irish decides to turn their back on their own people and land, they convert to Protestantism with the English monarch as head of their Church and state.

No, it's not just religious differences. Religion is used as an easy identifying feature of the two communities. One side is unionist, wanting Northern Ireland to stay in the United Kingdom with Great Britain. Most of these people are protestant descendants of planters from Scotland and England back in the 17th century. The other side is nationalist, and they want Northern Ireland to be part of the Irish Republic. Most of these are Catholic "native Irish."

A big part of the tension came from the Protestant side perceiving Catholicism as not just a religion, but as a powerful political force under the influence of Rome. The Protestant Unionists in the North did not want to be subsumed into a majority Catholic Irish republic because they were afraid of becoming an oppressed minority and having their rights trampled on.

In the last hundred years or so these divisions became more entrenched, with the protestant community coming to self-identify as "British," and with "Irishness" being promoted as an ethnic identity that only means Gaelic and Catholic. But go back a little further to the 18th century and many of the protestants were okay with being considered "Irishmen" since that's where they lived. And of course there were Catholics who supported union with Great Britain. And there were some conversions from one religion to another and vice versa, and some intermarriage.

Ironically, in recent years with the Catholic church losing a big amount of influence in the Irish republic, and society there becoming much more liberal and secular, the republic is probably not religious *enough* for the tastes of the Protestant Unionists in the north.