Contrary to popular misconception, there is not and never was a law against the monarch's being married to a divorced person. The kerfuffle surrounding the Abdication in 1936 involved great social and religious disapproval of divorce at the time. The monarch, for example, is the Supreme Governor of the Church of England, which back then prohibited the religious remarriage of the divorced. How, people wondered, could he or she be married in a civil ceremony?
The fact that Wallis Simpson was TWICE-divorced and also American played a role, too, and of course there's the view that some people were looking for any good excuse to get rid of Edward. If he hadn't been so problematic a personality, and if his lady love had been a once-divorced British woman, who knows? Perhaps some accommodation would have been made.
Since then, social attitudes towards divorce have changed hugely, and the C of E has dropped its blanket prohibition of the religious remarriage of the divorced. Fully three of the Queen's children have been divorced and two have remarried. It would be rather hypocritical for the British to insist that Charles couldn't be their king, and Camilla their queen consort, when so many British citizens have also been divorced and when there is no law against it.
As for Camilla's status, the UK does not have morganatic marriage whereby a wife gets a lesser title than the one she would normally have. Right now, she is the legal Princess of Wales even though she doesn't use the title, and she will be the legal queen consort, whether she uses that title or not. Under British Common Law, a wife takes her titles and style from her husband's. However, it will be up to King Charles, in the end, what title she actually uses, and he may decide to go with the plan he once described, that she will use the title "Princess Consort," even though there's no precedent for it.
Parliament would have to pass an act to deprive Camilla legally of the title of "Queen Consort". That would raise some awkward issues. Since the grounds would have to be Camilla's adultery with a married prince -- there isn't any other justification -- Parliament would then have to consider whether that married prince was disqualified from becoming king because of HIS adultery. It would be a bit difficult to decide that he was, given how many British kings merrily committed adultery many times throughout their reigns. And if Charles can become king, why can't Camilla become queen consort? The double standard involved in any Parliamentary act penalizing Camilla alone would outrage many, regardless of their views of the adultery itself.