Being bared from holding the throne does not mean being bared from passing the rights to the throne to someone.
Although most states bared women from reigning, only a few of them bared transmission of the throne through women.
In 1135, one of the bastards of Henry I could have become king of England. After all, Henry of Transtamare was only a bastard of king Alfonso XI. William the conqueror was only a bastard of duke Robert of Normandy.
I think the rights or not of transmission of the throne through women or of women to reign was not the main problem of England. The main issue was rather violence and political murder :
- the war beteween the sons of William the conqueror,
- the war of succession after Henri I's death,
- the rebellions of Henri II's sons against their father,
- the murder of Arthur Plantagenet by his uncle king John,
- the murder of Edward II,
- the murder of Richard II,
- all the overthrowings and murders of the war of the two roses,
- Henry VIII's executions of nobles seen as opponents,
- Charles I's execution.
Don't need to wonder why Shakespeare was an englishman.