Current polling suggests differently. But even with apathy, the path to replacing the whole constitutional monarchy system is a lot more convoluted than people realise when they say 'get rid of the royal family'.
There's a whole separate thread on this that I started - would love your input on there.
So the system can technically be changed at any time - all the government has to do is decide to do it - but it's going to be messy, very very expensive and take a lot of time (up to a decade or more of upheaval) to unravel how the constitutional monarchy is intertwined in our various parts of public life.
So for a government to go ahead with something like this they need unwavering support for the change itself, no other pressing matters and confident that it won't tank their reelection prospects.
Basically, you need French / American Revolution levels of public energy for making such a change - it has to be way more important that anything else the general public want the government to concentrate their budget and time on.
The more likely scenario is it gets slimmed down gradually - ends up more in line with the Scandi monarchs - with perhaps in George's old age there's a move to change the public life areas piece by piece on a rolling schedule.
Unfortunately for republicans Charles has proved a lot more popular then it was thought - so if he is King for another 10-20 years (possibly on the more conservative side because of recent health) that takes us to 2030s.
There will be a surge of popularity for King William and Queen Catherine - and the Wales kids will be popular while they settle into adulthood. If William is 55-60 when he becomes King and lives to his 80s, that takes us into 2060/70s.
I won't be here anymore at that point so I guess I'll never know if there is a better chance for a republic after William or George.