You are of course, right but you need to accept that the the symbol implicit in the crown is perhaps more objectionable to the Nationalist community than the Union flag. Equally, the Red Hand may be the symbol for the province of Ulster but over time it has become the property of the Loyalist community. Compare with the Harp as a symbol for the Republic of Ireland/Eire. There's a well-known pub in the centre of Belfast called "The Crown" which has a mosaic representation of a crown on its threshold. The Nationalists (who used to frequent the pub) take great delight in walking on the symbol.It is supposed to be a compromise flag, no? I imagine the republican colours are equally unsatisfactory to unionists.
And under the arrangement that seems to be coming closer to establishment thus far ITTL, Northern Ireland is still a part of the United Kingdom.