This is specifically untrue in regards to parallels to Edward VIII; there the issue was that Wallis Simpson was divorced with ex-husbands still living, which at the time, the Church of England did not allow. Charles remarried long after Diana had died, and so is not subject to this restriction.

I'm not intimately familiar with British law, and there may be other reasons why his divorce would make him ineligible, but it would not be for the same reasons that Edward was considered controversial.

Also, as regards Henry VIII and divorce, apparently he used the power of the newly created Church of England to annul his marriages, rather than actually get divorced.