I wonder if people who express this sentiment will still be doing so when the pendulum swings so far the other way. Will you also be grateful for a massive register that exposes everyone who ever espoused views in favour of LGBT, multiculturalism, etc in a society that condemns and even prohibits such views?

Perhaps there's some Middle Eastern theocracy where this scenario exists already. Are you glad that Saudi Arabian trans activists will forever have a target on their backs?