Henry XIII Gets His Divorce From The Pope?

Relationships with the rest of Europe will depend on
1) How the marriage was annulled if with papal approval due to Katherine embracing a vow of chastity - Mary remaining legitimate and in the succession then it is business as usual. Henry vacillating between France and Spain as it suited him (and them).
2) An annullment on its own (over the head of Katherine's objections) is going to offend Charles V but real politics is going to mean if with Papal approvement Charles is going to have to put up with the fact for the moment as he has no grounds to really object.
Also in both cases foreign powers are going to probably be relieved that Henry has opted for a domestic marraige that is not going to upset the political balance on mainland Europe.

On religion -
Anne's religious leanings are much debated as is her relationship with Cranmer - however given Henry's view of himself and his religion any lutheran leanings will have to be supressed unless she wants to find herself facing heresy accusations.
Henry in any TL that provides for Papal approval for his seperation from Katherine is going to remain a devout son of the church.
Unless at some future point he needs another marital problem sorting and the church refuses to help (assuming say Anne fails to provide a male heir and pops her clogs in childbirth or somesuch and Henry takes a third foreign bride)
He is though going to face some severe financial issues towards the end of his reign (without that flood of monastic wealth and land) and many of the Tudor courts self-made men are going to fail to advance their families without grabbing those monastic lands.
I think you are likely to see an increasing influence of Lutheran and reformist thought outside the court particularly amongst traders and merchants who have strong links to the continent that may over time lead to some form of reform but i would think England will probably follow the Scots reform example and might end in the same situation - though it is possible that a later Tudor King or Queen might see the advantages of controlling both church and state.
 
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