This isn't really a doctrinal change; they're two very different situations. As I explained in this previous answer regarding Henry VIII:

Well, it was never solely about finding a younger woman who could try for years and years to have sons. For one thing, Henry believed that if he were with the right woman and God blessed their union, a son would be granted to them. Remember that a major factor in his stated reasoning for divorcing Catherine of Aragon was that he claimed to believe she and his brother had consummated their marriage, and that therefore he had sinned by marrying her and was being punished with daughters, stillbirths, and children who died young. If he corrected his error, then God would be like, "Now we're good!" and provide a healthy, male heir to the throne.

When Henry met Anne, she was about 25 (and he was about 35), and he was highly attracted to her. She initially rejected his advances on the grounds that good girls don't get involved in extramarital/premarital relationships, which led to his desire to make her his mistress morphing into a desire to make her his wife, and despite the fact that it took seven years, he followed through. Catherine's track record of unsuccessful pregnancies and apparent menopause were a large factor in his interest in a younger bride, but by all accounts Henry was in love with Anne. His feelings were strong enough to keep the unconsummated relationship going for years and to result in a massive break from the Catholic Church and from an alliance with Spain and the Holy Roman Empire. And at the same time, 32 is not old for childbearing - certainly it would have been an unusual age for a first birth, but women typically gave birth into their thirties. Given that Anne became pregnant pretty much right away after the marriage, it seemed reasonable to believe that the problem was fixed.

By the time Jane came around, Henry had had time to reconsider. The theory had been that if Henry ended his marriage to "his brother's wife" and took up with someone not related to him, he would get a son. Instead, after he married Anne, they had a daughter and three miscarriages. Was God still disapproving? Henry was attracted to other women, as he had been in his previous marriage, and set his sights on Jane Seymour, who was one of Anne's ladies in waiting, not related to him in any way, and not associated with Anne and the break with the Church. She was also well within her childbearing window, as evidenced by the fact that she gave birth a year after the marriage to a son who was healthy enough to survive his childhood. All of these factors were important.

We tend to Other historical periods by exaggerating the average age disparity between marriage partners, redrawing the marital pattern to be about middle-aged men seeking the youngest and most fertile wives, and we also like to draw firm distinctions between marrying for love/attraction and marrying for other purposes. Reality is much more complicated, with multiple reasons for a choice of spouse coming together frequently. In any event, Henry's reasoning was that he didn't need to have a wife who was at peak fertility or young enough to allow for twenty years of trying for an heir: she just needed to be able to give birth once or twice, and if the marriage was sound according to God those births would be male.

tl;dr: The break with Rome was more about saying "the king can annul his own marriages if they're problematic" than about legalizing divorce. Because, in fact, when Henry ended his marriages to Catherine of Aragon and Anne of Cleves, he annulled them - he didn't divorce the women, he claimed that the marriages never truly happened in the first place, to Catherine because she was his brother's wife and to Anne because they never consummated it.

But centuries later, the situation was entirely different. To quote from another answer of mine:

As a couple, Edward tried to be with Wallis as much as possible in a way that added to the anxiety. He was devoted to her to such an extent that it seemed to degrade his dignity and imply more unfitness for the role of king - waiting on her hand and foot, allowing her to scold and mock him, and often relying on her to interpret current events and paperwork for him - and many have theorized some kind of BDSM thing (because of course they have). Once his father died and he became king in January 1936, things got worse in the eyes of the old guard. Mainly this lay in Edward's decisions to modernize or democratize the monarchy by breaking established protocols when he felt like it; Wallis also had a tendency to take charge and make decisions or statements that were casual to the point of being tactless. This played very well in the couple's small society, but was not well-liked outside of it, and may have made Edward more ready to be rude in similar ways. It was also becoming clearer to the civil servants who ran the government with the king that he didn't really have the intellectual energy for the job, and even in early 1936 there were concerns about Wallis's access to state papers and closeness to German ambassadors.

But he was truly intent on marrying her and making her queen. About a month after the death of his father, Edward told Wallis's husband that he planned to be crowned with "Wallis at [his] side", and in April he told her that "my Prime Minister must meet my future wife." A few months later, Wallis got her divorce rolling. Cocooned in his high-flying social circle, Edward had no real idea that many people knew about the affair and found it ridiculous or shameful, and that divorces were still viewed with repulsion by the working and middle classes. By the time he brought her with him in the autumn to Balmoral - a place still very much associated with Queen Victoria, where the wider royal family would spend time together - it was clearer than ever that he planned to make her queen, and the snubs were becoming more pointed in response. Things got even worse when she actually appeared in court to win her divorce and blatantly lied about not having committed adultery herself (a necessary step for a woman initiating a divorce, and the woman had to be the one to initiate it to save any face afterward), which upset the public deeply - particularly women, who saw it as a double standard that wouldn't be available to them in the same-but-not-royal circumstances. The British press had kept the details of the entire affair relatively hushed up, but they were starting to find it impossible.

By the end of the year, Wallis was strongly considering breaking off the semi-engagement to avoid being The Woman Who Destroyed A King, but Edward was threatening to toss his position and come after her rather than lose her. They had spent 1936 pretending that they could live like any aristocratic couple and that they were very popular, and finally had to face up to the facts: they couldn't and weren't, so much so that Wallis was in very real fear of injury or assassination when she went out. The Church of England did not recognize divorces at the time, and since Ernest Simpson was still alive, the archbishops regarded Wallis as still married, and would not perform the wedding. A morganatic marriage - one where the king's wife was only "the king's wife" and not the queen, more of a continental tradition than an English one - was put forward, but some of the officials in the commonwealth (Australian, South African, Canadian) who would have had to agree to it vehemently did not, and felt that abdication was preferable, since the king made it clear that either he would either marry her or leave. In the end, he abdicated.

And another:

So when Edward VIII prepared to marry Wallis Simpson, the real issue was her sexual behavior, her divorce, and her origins. The Church of England reluctantly allowed remarriage after divorce, but frowned heavily on it, and as it is the state religion, he was expected to follow its publicly-visible tenets as closely as possible. Wallis was not only a divorcée (in a time when divorces were still fairly scandalous), but a double divorcée with two living husbands. She was also foreign and not a princess, where precedent was for English royalty to either marry foreign princesses or titled Englishwomen: Americans rich from trade did not come into it. The two had also been involved in a long sexual relationship of the sort that was acceptable between a prince and a mistress, but not a prince and a future wife; she also was believed to have slept with other people while she was in the relationship with him. Basically, Wallis Simpson didn't fit the expectations for an English queen to any degree, and the church was far too hidebound to accept the entire package - it was threatened by her, and there was no cloak of propriety that would cover all of the problems. The public wasn't confronted with Dorothea Jordan and Lillie Langtry as the consorts of their king but as actresses, whereas they would have seen and heard about Queen Wallis the Divorced very, very frequently. It's also important that the aristocratic and governmental class as a whole disapproved; he didn't abdicate for her just because of the church, but because pretty much everyone in power was against the match.

tl;dr: It's one thing for a king to have had a sexual relationship with multiple people, and it was another for a future queen to have done so.