We probably don't look to the British Royal Family for progressive attitudes on anything, let alone the idea of girls taking up the throne. If a Royal marries a Catholic, or indeed anyone who is not a Protestant (but it seems a special mention of Catholics need be made), then he or she forfeits a place in line to the throne. With the upcoming marriage of Prince William to Kate Middleton, which is taken as a gateway to imminent reproduction, the discrimination against Royal daughers has come into focus again.
As it currently stands, if William and Kate should have a daughter first and subsequently a son, the daughter would have to become accustomed to the little brother they've been pushing around becoming the British monarch in the future. I hadn't thought too much about the rules of succession because recent British history is dominated is dominated by the rule of strong, publicly admired Queens. We've had Elizabeth II on the throne since 1952 and Queen Victoria was an adored monarch from the age of 18 until her death in 1901. They are really only accidental rulers in that no male sons stood ahead of them in the line of successtion. Though both had highs and lows during their reigns, there doesn't seem to be any case to suggest that the nation or the Commonwealth is subject to any detriment in having a Queen instead of a King in place.
Of course, we can argue that the British monarchy is a redundant institution in any case. In Commonwealth nations especially, the impact of the British Royal Family is ever declining, with the backs of coins and the annual Queen's birthday holiday constituting the majority of our interaction with the monarchy. Though there might be some formal effects on our political system, such as the Governor-General as the Queen's representative, our lived experience is such that we could easily forget we even have a Queen.
Perhaps for this reason it might never be possible to change the rule of succession to eliminate discrimination on religious and gender grounds. According to recent news stories, such a change would require all fifteen independent Commonwealth nations to agree. The question is whether all would devote the time and effort to altering rules for a monarchy that many no longer wish to be involved with.
Nevertheless, though Australia is perhaps more concerned with becoming a Republic and changing the flag to remove the Union Jack, for so long as we remain in the Commonwealth it would be nice if such blatant discrimination against daughters were removed.