That is such a tough question to answer. The main theories are:-
1) Anne's faith was more political than religious - “Self-interest and ambition – which Anne had in plenty – each pointed to reform as the cause that would serve her best” G W Bernard
2) Anne's reformist faith was real - “It is, indeed, hard to deny Anne a personal faith. Apart from the Bible in which, significantly, we know she had an interest in Paul’s epistles, the works she read and collected are certainly redolent of a Christianity of commitment and not of routine observance.” Eric Ives, and “If this was Anne Boleyn’s experience of faith, then she was evangelical by conviction and not just policy.” Eric Ives
3) She was Catholic - G W Bernard believes that Anne's observance of Catholci rituals, and her almoner's (John Skip's) defence of them in a sermon, shows that she was Catholic rather than an evangelical reformer.
You can read more in my article "Anne Boleyn's Faith" at https://www.theanneboleynfiles.com/anne-boleyns-faith/4990/ and "Anne Boleyn and the Reformation" at https://www.theanneboleynfiles.com/anne-boleyn-and-the-reformation/4978/ but I believe that Anne's collection of reformist and "heretic" literature, her links with Protestants in Europe, her use of Tyndale's New Testament and the way she encouraged her ladies to read the Bible in English, her support of Protestant refugees and her support of the appointment of evangelical bishops etc. all point to her being an evangelical reformer.
It is so hard to label Anne, when the Protestant Church as we know it today did not exist then. I'm not sure that either a Catholic label or a Protestant label would fit Anne properly. She was not entirely Lutheran but she was certainly evangelical and looking for reform in the Church.
