Don’t confuse Elizabeth with Jane Grey. Lady Jane was, like Edward, pious, as was the Catholic Mary, but Elizabeth was a political animal. You should know that no one every accused her of piety. For about ten years she held out the possibility that she might marry a Catholic prince. That ended, of course, after Pope Pius V, denounced her as a heretic. She had, of course, by that time renounced the Spanish alliance and had begun to intervene in the Netherlands and she would do what she could to helpo the Huguenots in France. Soon she would legitimize the piracy of Drake and others. As for her religious policy is concerned, England was slowly turning Protestant as the older generations died off. The Jesuits had entered the country both to rally the Catholics and to undermine her government. But the defeat of the Armada affirmed the Protestant Character of England and the Guy Fawkes episode—talk about a 9/11 event—discredited Catholicism.
A political animal? Of course, she was the queen of England. It was her political skills that made her one of the most effective sovereigns in English history. And she had no intention of marrying a Catholic king. She keep lots of man hanging on, with the hope all in the other direction.