Can you define to me what "the UK" is? To me, any country is its people. Nothing more, nothing less. Hating the government or its laws or its institutions doesn't equate to hating the country. Those things exist to serve the people. A person might love the people so much that he believes the laws and institutions are so unjust that they need to be gotten rid of and replaced, to better serve the people.
I disagree, there is far more to a country than simply its people. There is a culture and a history and usually even a language as well to give her and her people an identity. I was not implying that republicans hate the UK people, merely one aspect of the UK's identity, the monarchy. They might not hate the other stuff either.