It's not so simple. I don't automatically support any given team based on whether I pledge allegiance to any given country.
For example, back in the day when he was good, if Wayne Ferreira (SA) was playing Tim Henman I would support Henman. Why? Because he is a better sportsman, and I don't like Ferreira because he is sullen and moody. That doen't mean that the South African authorities will be demanding that I relinquish my South African passport, it just means that I am not a fan of Wayne Ferreira.
The same applies to other sports. Just because I support Australia in the cricket against England, doesn't mean they have my automatic support for all other supports, such as swimming for example. It comes down to the team, and whether I like them or not. Just because a team represents a nation in a particular contest, doesn't grant that team 'immunity' from criticism, even from its own citizens.
I'm not a British citizen yet, but when I become one, I'll be looking out for little clauses in the oath that I must swear, just to make sure that I am not automatically expected to support the England cricket team with patriotic fervour. ;-)