Some further clarification about the religious requirements for succeeding to the British throne:
1. The
Act of Settlement of 1700 stipulates that the British crown may only descend to
Protestant descendants of Princess Sophia. Any person who is not a Protestant at the moment of the prior monarch's death or abdication will be bypassed for the succession to the throne.
This eliminates members of any Christian church that is incompatible with Protestant Christianity (Eastern Orthodox, Roman Catholic, Jehovah's Witness, etc.) as well as people who have no religious affiliation.
the Crown and Regall Government of the said Kingdoms of England France and Ireland and of the Dominions thereunto belonging with the Royall State and Dignity of the said Realms and all Honours Stiles Titles Regalities Prerogatives Powers Jurisdictions and Authorities to the same belonging and appertaining shall be remain and continue to the said most Excellent Princess Sophia and the Heirs of Her Body being Protestants
2. The
Bill of Rights of 1688 specifies that a Roman Catholic is
forever incapable of succeeding to the throne. This means that even if a Roman Catholic converts to Protestantism and remains a Protestant at the moment of the prior monarch's death or abdication, he or she will still be unable to succeed to the throne.
This "forever" exclusion is specific to (ex-)Catholics. Orthodox Christians, Jews, Muslims, non-religious people, and so forth all have the option to convert to Protestant Christianity in order to enjoy succession rights to the British throne (so long as they have never been Catholics).
That all and every person and persons that is are or shall be reconciled to or shall hold Communion with the See or Church of Rome or shall professe the Popish Religion F3... shall be excluded and be for ever uncapeable to inherit possesse or enjoy the Crowne and Government of this Realme and Ireland and the Dominions thereunto belonging or any part of the same or to have use or exercise any Regall Power Authoritie or Jurisdiction within the same
3. The Act of Settlement of 1700 also requires the monarch to be in communion with the Church of England.
That whosoever shall hereafter come to the possession of this crown shall joyn in communion with the Church of England as by law established
At the time the Act of Settlement was enacted, only members of the Church of England itself were admitted to Holy Communion in the Church of England (
refer to page 13 of this parliamentary research briefing from 2009). Therefore, the "communion" requirement in the Act of Settlement originally meant that the monarch was obliged to be a member of the Church of England.
Today, however, the Church of England admits to Holy Communion any baptized Christians who are members in good standing of a Christian church that subscribes to the doctrine of the "Holy Trinity" (which would mean that even Catholic and Orthodox Christians can be admitted to Communion in the Church of England). Therefore, by today's standards, anyone who meets the "Protestant" requirement the Act of Settlement of 1700 will probably meet the "communion" requirement in the same Act.
https://www.churchofengland.org/more/policy-and-thinking/canons-church-england/section-b
As for the Episcopal Church: The Episcopal Church is a member of the Anglican Communion. It was formed from American churches belonging to the Church of England which, after the American Revolution against the British crown, began to self-govern and renamed themselves from Church of England to Episcopal Church for obvious political reasons. The separation was political, not theological. Religiously, Episcopalians are Anglicans.
Read more about the Episcopal Church of the United States of America:
https://www.episcopalchurch.org/who-we-are/history-episcopal-church/american-church/