Looking for a term for "not supporting the country you're currently staying in"
I remember reading a term(derogatory) which was predominantly used in Britain, if I'm not wrong, that is used to talk about people who have immigrated to Britain but do not support the British sport teams, but instead support the country's team that the person has emigrated from, especially when the particular country is playing against Britain.
This isn't an adjective or epithet, but captures the idea:
(pass/fail the) cricket test
British Asian athletes and fans in particular have long been subject to racialized nationalist arguments about allegiance and assimilation demonstrated through sport team membership/fandom. Conservative British politician Norman Tebbit controversially framed issues of allegiance and assimilation for British 'immigrants' in terms of a 'cricket test':
"A large proportion of Britain's Asian population fails to pass the cricket test. Which side do they cheer for? It's an interesting test. Are you still harking back to where you came from or where you are?" (April 1990, Los Angeles Times interview). ref.