Northern Ireland isn’t in a political crisis in relation to them being in the YK, it’s their inability to agree on local governance.
Also Scotland might not consider themselves to be British, but they are part of the nation and when the vote happened it was as the country of he United Kingdom, not as England, Scotland etc. Let’s just put it this way, if We had all remained because Scotland wanted to remain then wouldn’t England be being kept against their will? But that would be okay? Scotland might be a separate cultural identity , but the political identity is still that of the UK.