Swamji said in one of his talks that "Do I wish that the Christian would become Hindu? God forbid." I hear this in the context of his talk and I think that is exactly what his is wishing. I think he does want Christians and Muslims to become Hindu in one very essential way. He wants them to be non-dogmatic, open minded and accepting of the validity of all religions. He wants Christians and Muslims to embrace religious diversity as an expression of divine plurality and creativity. He wants Christians and Muslims to have a very Hindu view of other religions. But that is not what Christianity or Islam wants. They are both very much invested in the idea that their way is the best and/or only way as given by God to live a religious life.
For Christianity to acknowledge that other incarnations of God exist and that there are equally valid ways to God outside of Jesus completely undermines most every tenant of Christianity. Christianity would no longer be Christianity if it would change its worldview to accommodate what Swami Vivekananda is suggesting in his talks. For a Christian to see the world religions in the light of what Swamiji is suggesting would involve a lot of very mushy thinking on their part. Christian theologians would have to do crazy mental acrobatics to keep their dogma intact (which is absolutely central to Christianity) and have the open and broad mindedness of Swamiji's.
What I have noticed is that people from a Hindu mindset do not take into account the importance of belief for those who are Christian or Muslim. For a Hindu, belief is not central, experience is. Hindus aim to experience God directly. For a Christian, belief is very central. In fact, it is the cornerstone of their salvation. Direct experience of God is nice but in no way is it essential for salvation. To suggest that a plurality of beliefs are equally viable for attaining salvation is just ridiculous from a Christian point of view (and I would imagine the same from an Islamic point of view). So, does Swamiji "wish that the Christian would become Hindu?" I would say, yes. He does. At least he wants them to view Christianity from a Hindu perspective, not from a Christian one.
I am writing this to get other's thoughts and perspectives.