The tradition of Six Preachers was established by Archbishop of Canterbury Thomas Cranmer in the sixteenth century. I could find little information about the collection of posts on the Web, but Wikipedia does offer a brief article. It is unclear whether any of the Six Preachers over the years have been other than English clerics.
In the letter, PEP complains that the appointment of Baucum enhances the dubious claim of ACNA to be Anglican and is accepting of the interference of the Church of Nigeria (Anglican Communion) in the affairs of The Episcopal Church:
Our primary concern is not Dr. Baucum’s personal talents or accomplishments but his associations. He is in the rather odd position of claiming to be a priest of two churches, the schismatic Anglican Church of North America and the transgressive Church of Nigeria (Anglican Communion). The former has established itself largely by poaching souls and real estate from The Episcopal Church and continues to be involved in property litigation with The Episcopal Church, a matter of apparent indifference to Canterbury. The Church of Nigeria, on the other hand, has proven equally predatory regarding our own church and has flouted longstanding Anglican tradition regarding boundary crossings. Moreover, this honor bestowed on a putative Nigerian priest comes at a time when Anglican leaders in Nigeria are applauding the advent of a new law persecuting homosexuals and advocates for human rights.PEP’s letter asks Welby to withdraw the appointment or, at the very least, to make it clear that it is a strictly personal one. PEP also asked the archbishop to speak out against the recently enacted anti-homosexual law in Nigeria.
The full text of the letter is included in Mark Harris’s post. A PDF copy of the letter can be found here.