Hmm this is true, though could having a Protestant wife, with his kids being firmly in the Anglican camp, perhaps help assuage some of that tension?Personally, I think Charles is still likely to be unpopular and his reign a bit of a mess. Though I imagine that, without a Catholic mother, the next generation of Stuarts will be less inclined to Catholicism. Also, are we sure Anne would be called Princess Royal? IIRC that was a direct importation from France via Henrietta Maria.
And you're right, it was brought in by Henrietta Maria, my bad.
I'd actually be quite interested to see what else could change due to this marriage, with Sophie obviously being a blank slate.