I really don't feel it's a big political statement to accept an invitation to perform for royalty of 'another' country, so much as it is to reject an invitation. Canada and England have had their 'given' relationship for a very long time
... and my understanding is that the monarchy isn't really about politics, but rather simply a centuries-old institution. Parliament, however, is about politics.
While it's certainly true that the United Kingdom and Canada are separate countries, Canada is still one of the Commonwealth realms (that's not the same as being a member in the Commonwealth of Nations, there are only 16 Commonwealth realms, and 54 Commonwealth nations) and as such, Elizabeth II is also the Queen of Canada (and of Australia, New Zealand, Jamaica, Papua New Guinea, and several other countries).
So yeah, he's a citizen of another country, but if he performed for her, he'd still be performing for his queen.
I don't know if Cohen's a monarchist, a republican, or doesn't care, of course. So he may or may not consider her to be his monarch, but legally speaking, that's how it works. Don't take this to indicate that the royal family has any particular power or influence in Canada (beyond that of any other famous person with ready accecss to mass communication, of course) or any other non-UK commonwealth realm (and the degree of their influence in the UK is debatable as well), but in the form of law, she's the queen of Canada and is represented there by her Governor-General, who carries out her wishes as regards that nation. In practice, obviously, the Prime Minister runs the show and the Governor-General defers to that individual. The retention of the monarchy, especially in modern constitutional monarchies, is generally a function of two things: 1) tradition and 2) practicality. These systems work, and most governments are loath to change working systems to ones that might go haywire and all crazypants.