The English throne has a history of using regencies, not abdications for elderly monarchs. Also if Charles wants to avoid the throne, he has a very available out to him. Given his association with Greek Orthodoxy via his father, if he converted to being an Orthodox Catholic, he would not be Protestant and thus under the Act of Settlement incapable of assuming the throne, but since he wouldn't have committed the heresy of becoming a Papist, Princes William and Henry could still take the throne.
Actually, Orthodox Christianity does not violate the Act. It is specific to Communion with Rome. Or a papist. http://www.statutelaw.gov.uk/content.aspx?activeTextDocId=1565208
I think the Orthodox Church was in Communion with the Anglican Communion, at least until they started ordaining women.
There are two separate provisions in the Act of Settlement that are relevant, the first, which would bar not only Charles but also Henry and William from the throne of Charles became a Roman Catholic is:
However, a further restriction is that:
That could be viewed as including other churches in full communion with the Church of England, such as those in the Anglican and Porvoo Communions and the Union of Utrecht. However, relations with the Orthodox have been warmer than those with the Papists, but there never was full communion and the relationship has grown colder as the Orthodox and Roman churches have grown closer.
So if Charles became Greek Orthodox, that would bar him personally from the throne, but not his issue.