A question about reincarnation

Hello everyone, I am a writer doing some research for a book and had a few questions about the concepts of Reincarnation.

In the world we are building there is a new technology which makes everyone functionally immortal and this technology is thrust upon the American people as a whole.

My question is, how would this affect those of Hindu faith? Because there is a component of Reincarnation, would Hindu people be upset by the technology? What questions would this raise within the faith? How would an average Hindu person react to this technology and the idea that they would no longer be able to come into new bodies?