Elizabeth Tudor could have been executed during Mary reign simple because she did not want to change her faith and become a catholic.
Her reluctance to convert to Catholicism made Mary wary of Elizabeth and dislike having her as her heir, but really Mary was also vigilant of her because of Elizabeths connections to treason in 1554. Elizabeth was imprisoned and interrogated in the Tower because of the evidence suggesting her involvement with Thomas Wyatt a figure head in the rebellion of 1554 and not because she was a Protestant of sorts.
But overall this was period where Catholic and Protestant monarchs did persecute their religious opponents for theological and political reasons.
Noli me tangere; for Caesar's I am

Unfortunely this was common place in the tudor era. Jane was not the only person to have died for her faith or views to the sucession. There were many others. Mary Tudor could have been executed if she did not back down when her father Henry V111 declared her a bastard. Elizabeth Tudor could have been executed during Mary reign simple because she did not want to change her faith and become a catholic. Thomas More, Cranmer, Buckinghamshire, Ann Boleyn and Catherine Howard. Yes, it was a dark period of history but an interesting one.
I enjoyed the film of Lady Jane.
The best films are made in an intelligent format.