The Queen should no longer be Supreme Governor of the Church of England, a radical report says.
The commission talked to Buckingham Palace officials
A year-long inquiry into the future of the monarchy also suggested the centuries-old ban on a Catholic monarch should be lifted.
The proposals are among a series of far-reaching changes recommended by the Fabian Society.
However, the left-wing think tank fell short of suggesting the abolition of the Royal Family.
Among other recommendations, the Fabian Society suggested that royals should pay inheritance tax and the principle that sons of sovereigns and their descendants have precedence over daughters in succeeding to the throne should be scrapped.
So, if Prince William's first child was a girl, she would automatically one day be Queen.
The commission took evidence from a range of people - including Buckingham Palace officials.
Buckingham Palace said: "The report is a useful contribution to the debate on
changes to the monarchy.
"We will be interested in seeing public reaction."
Under the proposals, if Prince William's first child was female she could be Queen
It considered a range of subjects, including public attitudes to the Royal Family.
BBC correspondent Jane Hughes said that while the report would provoke debate it was unlikely that the changes would happen soon, if at all.
Many, such as recommending the opening of Parliament should not be held every year, would require changes to legislation.
The Fabian Society was struck by the weight of continuing support for the monarchy, but warned that without reform the institution's strength might decline quite quickly, BBC royal correspondent Peter Hunt said.
Michael Jacobs, general secretary of the Fabian Society, told BBC News Online the monarchy had to reflect British society.
"We've had a lot of constitutional reform and we need to make sure the head of state is part of that process.
"The monarchy is tied to the Anglican church at a time when most people are not part of it. The monarch should not be head of the Church of England but should have a more neutral relationship with all faiths.
"We've also proposed that the rules of succession should be changed so that eldest daughters and Catholics should no longer be barred from the throne. These discriminatory rules are inappropriate in the 21st Century.
"The aim of the report is to stimulate public debate and I am delighted to see that Buckingham Palace has described it as a 'useful contribution'."
'Defender of faiths'
Prince Charles is known to be keen to modernise the monarchy and has spoken about being a "defender of faiths" rather than Supreme Governor of the Church of England.
Under current rules, Charles would become head of the Church upon his succession to the throne - a move which, commentators have often remarked, casts a significant shadow over his relationship with Camilla Parker Bowles.
The Church has strict rules on the remarriage of divorcees, and because of this, if Charles were to marry Camilla, his moral authority as head of the Church would be under threat.
The commission was led by barrister David Bean, and included Labour peer Lord Waheed Ali, constitutional historian Lord Kenneth Morgan and Professor Dawn Oliver, constitutional law expert at University College, London.