Well, no, I don't automatically support anyone's celebration of their cultural identity and heritage. Some societies' culture and heritage - or, at least, the way some people in those societies choose to understand or celebrate it - is horrible. Taliban culture, or Confederate heritage, or 21c. Russian nationalism are pretty obvious things we all recoil against, aren't they?
As I am British and English, I understand the nuances of British culture better than any other. To be clear, I am obviously not comparing the monarchy to the Taliban! But part of the British tradition I appreciate greatly is the right to disagree. I disagree with the institution of the monarchy. I disagree with the veneration of a military which is linked so closely to both terrible colonial crimes, as well as heroic derring-do.
So I am not recoiling at "Englishness" or "Britishness" or The English or The British. I am as English and British as they come. But Trooping The Colour is a particular flavour of Britishness which I don't care for. So I do find it odd that people say they are proud of something British just because it is British, without considering what it is.
So, sure, our militaristic colonial history has sure made us good at marching in straight lines while playing bombastic music on horseback in front of a man who is the head of our country because his mum was and her dad was and his brother was. But none of these things fill me with pride. They feel distant and irrelevant to my English life.
(And it's just reductive and silly to conflate the emotional and transactional relationships we have to the nation state. I don't hate the nation state. I just don't pin my personal or cultural identity to it. I am not keen to do away with the NHS, just as I am not keen to get rid of the National Grid or Network Rail., because they are hugely invaluable modern institutions that keep our lives running. But I'm not going to stand on a street corner waving a flag for our National Grid and insisting it is a thing of great pride when compared to Germany's or Canada's or South Korea's.