As far as I know they sort of get to believe what they want. Seems wierd to me, we don’t have too many of those folk here in the UK.
Sounds rather like the Church of England. It has no doctrine either, whether
de fide (of the faith) or
de moribus (of morals). In fact, if someone presumes to claim anything that ‘all Anglicans must believe’, he or she will likely be scorned by some as intolerant. In its attempt to be a politically and religiously neutral Established Church for everyone, eg the Elizabethan Settlement, it has ceased to offer anything specifically Christian to anyone, having no dogmas. Even the Creeds are not enforcible. Anglican Bishops have denied the Trinity, the Resurrection,. et al, without consequence. That means those denials are acceptable for Anglicans.
Everyone decides for him- or herself what’s right. They hide behind a sort of tacit
sola scriptura argument for authority, but in the end, having no confessional theology, apart a dated Calvinist diatribe called ‘The Articles of Religion’ (variously permutated), they are no different than New Age or Unitarian Universalists. Or Buddhists come to that.
Mind you most Anglicans aren’t atheists though they can’t be bothered to explain why they believe. Again, it’s all about personal faith and no pontificating please, which in a culture which considers discussing religion incivil, it’s also politically correct to believe for no reason that one can explain. One mustn’t explain. Evangelical Anglicans do, of course, but it isn’t characteristic of Anglicanism as such. And Evangelicals are a bit of a bore, really. And just about all Anglo-Catholics who believe in Catholic faith and morals have left for Rome or are in the process of converting.
Case in point. Two atheists, who have never been previously married, and who live – doubtless cohabiting – in their legally defined Anglican parish, are entitled by law to a Christian marriage in their parish church by a CofE priest. Neither belief nor baptism is required. A previous marriage is not an obstacle if the Vicar approves the remarriage. At his or her discretion. Yes, each Vicar is a Marriage Tribunal. Just as each Anglican is his own
magisterium and Pope.
So, to answer your question, Anglicanism. being – by law --tolerant to the option of atheism as just another expression of religious belief, is therefore, tacitly, an Atheist Church (though, again, most practising Anglicans are not atheists).