God save the Queen innit m8.
It is tradition, you wouldn't get it. It's a symbol of our former glory. Something that gives us an identity, and a connection to the past. Spiritually too, the monarch is the head of the church. The royal family is important because of those factors. You globohomos won't succeed in washing away what it means to be an Englishman.
Surely you'd still have most of the relics of that tradition/former glory without literally having some extra-chromosomed, buck toothed rich family living off taxpayer dollars in government property.
Your national identity might even be more accessible if average folk could actually step foot in Buckingham Palace.
What about the head of the church part? https://en.wikipedia.org/wiki/Church_of_England
The royal family represents a dignified symbol of the UK's past as well.
Honestly, if you are against them you are against Britain, plain and simple.
Didn't Henry VIII establish the Church of England so he could remarry? Plus I've read that UK attitudes are trending towards secularism and that affiliation with the COE is heavily in decline.
I actually didn't even know that the monarch is still considered the head of the church, but that makes sense since it was established by a monarch to suit his own agenda.