I could write quite a lot, mostly griping about the inconsistency of the position of the most vocal commenters, or their ignorance of the current position of the Church of England.
Charles's position, as an Anglican, is clear -- as a widower, he is free to remarry.
Camilla's position is less clear.
The position of the Anglican Church is as follows: The decision whether or not a divorcee may remarry is a matter for the parish priest, as guided by his/her bishop. The priest is expected to take into account whether or not the divorced party was "responsible" for the divorce -- so that, for example, a person who was involved in a divorce as a result of the other party's infidelity might expect to be looked on more favourably than a party who was unfaithful.
I don't know the circumstances surrounding the divorce of Mr and Mrs Parker-Bowles, but I expect that the priest involved in the marriage will be familiar with the circumstances. (The priest, in this case, being Rowan Williams, the Archbishop of Canterbury)
I believe that in this case there is to be a civil marriage, followed by a blessing. This distinction is a total nonsense, since the Christian content of a blessing coincides 100% with a marriage. A priest who is unprepared to conduct a Christian marriage ought to be unprepared to conduct a blessing of its Civil equivalent. So I have to assume that, since the priest is prepared to bless the marriage, that it falls within the bounds of what is considered acceptable by the Anglican church.
Since I've not studied the circumstances closely, I'll assume the judgement of the priest (the archbishop) is sound.
So ... the fact that the Heir Apparent is to marry Mrs Parker-Bowles carries no implications for his role as Defender of the Faith, titular head of the Church of England. It carries no implications for his role as heir to the throne.
If they want to get married, they should feel free to go for it.
There are parallels with the situation of Edward VIII and Mrs Simpson -- but most of them are meaningless, since the position of the Church has changed since 1936.
I expect people to do their usual job, pointing out my incorrect assumptions, factual inaccuracies and logical flaws in the comments.