If the UK changes the rules of succession to the British Crown, what will the rest of the Commonwealth do?

If you didn't know, the Commonwealth nations that have the Queen as their head of state have their own distinct Monachies (although they are all currently made up of the same people). The current stance of the British government is that the rules of succession will only be changed if the Queen's other realms agree. But what if they did change it so that it was the first-born child (rather than the first-born son) that becomes Monarch? Could we end up with a situations where William and Catherine's daughter becomes Queen of Great Britain, but their son becomes King of Canada? Or do you think it's more likely that those countries would adopt a Republican system?