Well, the answer is yes, keep low profile, otherwise any Argentine is going to ask you what happend to the the aircraft carrier Invincible. You know, freedom of press is not so wide during war and as you can see, version are very different about it.
http://es.wikipedia.org/wiki/HMS_Invincible_%28R05%29
http://en.wikipedia.org/wiki/Invincible_class_aircraft_carrier#Falklands_War
However, here there is no doubt that it might be anything but not invencible.
Don t forget that the british invaded BA twice and they were defeated by BA citizens twice, so, it is a very bad idea to have high profile about Malvinas, otherwise any Argentine might remind you that the task force thought that they were comming for a camping and they lost many ships.
So, it s right, we have no issues with people who was born in the UK, this is an immigrant s country where a guy called William Brown is our navy national hero.
http://en.wikipedia.org/wiki/William_Brown_(admiral)
So, it is all about to be polite.
Regards