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The idea of this thread is simple. James II has a slightly stronger backbone and never converts to Catholicism. I know this might be almost ASB, but he was stubborn when he should've been pliant - so let's extend this to his religion as well, he's friendly to Charles II, and Anne Hyde still does, and when she dies, he still marries a Catholic second wife, but James himself doesn't actually take the final plunge. There's rumours that he is secretly papist - but AFAIK, there were rumors like that about Charles II as well - and all that. IMO James was more in favour of balance between Protestants and Catholics than anything else.
So, let's go with the idea that while he never converts, he's still following the same Catholic-friendly policy of OTL. Would he still end up being deposed?