It's fun doing hypotheticals on this. I'd actually argue that 'perpetual' humans would be
much less likely to explore the stars! Take, for instance, the people who recently died on the Titan. They knew they were taking a risk going on it. At least one of them had also recently flown on one of Bezos' rocket launches. Their mindset is really easy to understood, as it also happens to be my own.
They were looking to experience all that life could offer, because in the end - what's the worst that happens? Well you die, but you're going to die anyhow. And living a rich life, ended prematurely, seems infinitely more desirable than living a drawn out life, doing everything to minimize risk, where you die all the same but perhaps without having ever given yourself a chance to live.
But imagine those individuals could have reasonably expected they might be able to live forever. I expect there is exactly 0 chance they would have even considered going on that sub, in one of Bezos' rockets, or engaged in basically any activity with any possible risk whatsoever. Because suddenly what you're risking, your life, has literally infinite value unless you happen to be suicidal to begin with. And this would pose a major problem for society doing much of anything.
There's going to be a high rate of mortality for the first colonists on Mars because there's a zillion things that can go wrong, and we aren't going to be able to anticipate even a fraction of them. Who in the world would ever want to risk this if you could live forever?