As we begin to learn more and more about the human body, it becomes clear that the brain is not the only organ in charge of consciousness, so declaring an organism “alive” or “dead” based on brain function is a fallacy. That’s why medicine makes the formal (if not legal) distinction between “dead” and “brain dead”, and why organisms such as jelly-fish can be fully alive without ever having developed a brain.
The truth is that drawing the line between life and non-life is much more complicated than brain activity. Even in religion, it’s a complex question. Daoism declares the moment of inception as the beginning of life, while the Abrahamic religions (Christianity being one) draw then line at the moment of birth.
The whole abortion debate was only brought up as a side issue in the 1960’s in order to enrage the right-wing’s religious base to convince them to come out in droves and vote in favor of a segregationist Presidential candidate. Therefore, abortion and conservatism are linked more through the power of an advertising think-tank than on the actual basis of religion.