As noted by Sonia Arrison, the Pope is not in favor of engineered human longevity. Surprise, surprise:
Modern medical science strives, if not exactly to exclude death, at least to eliminate as many as possible of its causes, to postpone it further and further, to prolong life more and more. But let us reflect for a moment: what would it really be like if we were to succeed, perhaps not in excluding death totally, but in postponing it indefinitely, in reaching an age of several hundred years? Would that be a good thing? Humanity would become extraordinarily old, there would be no more room for youth. Capacity for innovation would die, and endless life would be no paradise, if anything a condemnation.
Which nicely frames three of the common mistaken, knee-jerk objections to greater longevity: the Tithonus Error, predictions of stagnation, and the expectation of boredom. These and other objections are easily answered - visit the links in this paragraph to see more of a discussion. One shouldn't expect a vested interest like the wealthy hierarchy of a modern organized religion to meaningfully engage the pro-longevity side of the debate, however. This will be to their detriment in the end: siding against medical progress and with the massive death and suffering caused by aging is a short term, conservative position for any organization, no matter how greatly they benefit from the status quo.
I'm dimly aware enough of the foundation of Christian theology to know that death and immortality have a central place in that grand structure of delusion and desire. It is not unexpected to see the vested power structure at the head of it all feel threatened by the prospect of a secular takeover of this core portion of their domain. One can look back at the history of cosmology to see how this process plays out between a rich and powerful faith and comparatively poor (but ultimately unstoppable) scientists and technologists. We can hope to see less in the way of murder this time round, though it could be argued that all attempts to hold back progress in the development of longevity science are a form of indirect mass murder.
I suspect that the fixation upon mortality sells short the diversity of the religious impulse, however - which makes position statements like that of the Pope above look very much like ossified short-termism within the upper reaches of the Catholic Church. Religion is a vast pearl grown over tens of thousands of years around a wide range of unsatisfactory irritants within the human condition and the nature of reality. Death is but one of those irritants, and Christianity but one gloss on the pearl's outer layer. For so long as humans remain largely human in the structure of mind and psychology, there will be a great demand for religion of one sort or another.
No matter your opinion on the topic, this is as it is, and one has to learn to live with it. The future is clear: death and all things pertaining to it will one day be as much in the domain of life scientists as cosmology is now in the domain of astrophysicists. The sooner we get there, the better.