The Monarchs' gender butterflies a fair bit politically. Even though the Monarch doesn't hold much power, the simple fact that you get anther King will have a major effect on politics and culture.
Assuming that Prince Matthew/King George VII lives for roughly the same time as Margret IoTL, then you'll have a reign lasting from 1953-2002. Also assuming that George VII has the same temperament and a similar personality as Margret (for the sake of the argument because the butterflies are in their hundreds), then you also have a fiercely intelligent elitist chain smoker lacking hubris, refers to Irish as Pigs, and conducts numerous extramarital affairs.