I think eliminating aging would probably bring more stability to society: people would stop forgetting the past so much, because there'd still be people around reminding them of it, who had personal experience. History tends to work in cycles, and a lot of that is because populations forget what they learned through experience, because the people who went through the experience die off and the younger generations don't learn the lesson properly. Sure, it might mean some change will be slower, but you'll also avoid highly damaging short-term aberrations (like the Nazis).

Also, you seem to believe that people never change their views. I don't think that's really true either; people do evolve over time. My views are very different than what they were when I was a teenager (and not more conservative either). Older people do adapt to changing society. Look at, for instance, the acceptance of various social changes in the US, such as gay marriage. These things did not come slowly; they were breathtakingly fast. There'd be some initial pioneers pushing it for a while, but not getting very far. But eventually, like a dam breaking after a crack, suddenly the whole society would adopt it. Go back in time 20 years and ask some random people if they think gay marriage would be legal nationwide by now and they'd think you're crazy. This didn't happen just because of some old people dying off; it happened because the entire society got comfortable with the idea, though it took many of them a while to accept it.

Finally, eliminating aging doesn't mean eliminating death or childbirth. People will still have children, and people will still die (from accidents, murder, diseases, etc.). Also, the biology of the brain that affects old peoples' thinking will presumably be altered by anti-aging treatments, making them think more like younger adults.