Quick question, if a GP started dry and became wet did they used to stop the race while everyone changed to wet tyres?

Only recently.

IIRC the first GP to be red flagged was Silverstone in 1973 due to an accident not rain. Nowadays they put out the safety car and only stop it if it's really dangerous.

Depends on how far back you go...

There was a time when the same tyres were used in both wet and dry.

Not a GP of course, but the 1951 International Trophy at Silverstone was stopped after 6 laps due to the torrential rain and hail. Duncan Hamilton, who was lying second at the time, was so convinced that the race would be restarted that he unwisely wagered Louis Giron all his second place prize money that the race would continue. (Source: Touch Wood)

It's rare that a safety car is deployed when an event goes from dry to wet, even nowadays. It usually takes a heavy downpour and/or accidents for that to occur.