The monarchy traditionally makes changes at a glacial pace even without taking into account any government debates/law changes that need to take place so I couldn't see any major changes happening quickly.
But hypotheticals aside, as I mentioned on the other thread, in the current state of the line of succession you've got first in line William with three seemingly healthy offspring. If he lives until only his 70s, the George will be in his mid 40s. If William follows his grandparents' good health and lives until 90, then George will be nearly 60 before he takes the throne.
Charlotte and Louis will both be in their 50s.
There's a good likelihood that one or more of those three have had children, potentially grandchildren even by then.
And a good 40 years to decide what to do re line of succession. A gay George and partner might have decided not to have children, or have had children in the acceptance that Charlotte will remain the heir. Same if he's not gay but infertile. He could decide he doesn't want to be the first openly gay monarch and abdicate his place in advance to Charlotte. They will all have plenty of time to think about it and prepare the next potential heirs for the role.
There would be absolutely no need for the shenanigans of past monarchs of hiding their sexuality with a lavender marriage because that was in the days where power grabs could come from foreign monarchs and domestic power hungry people leading to wars, invasions, instability etc, let alone being executed for failing at the 'top' job.