When considering insurance, one usually tries to estimate the cost of an event multiplied by the likelihood of an event. The insurance company needs to charge slightly more as a premium, but if it's not too much more, that's a good purchase. It's a good idea for individuals to trade a small amount of expected value for a big reduction in variance.
The odds of a nearby star exploding are fairly easy to calculate, as far as I know. I could inquire from a few astronomer friends if you'd like. It's probably on Wikipedia, too. The cost of avoiding a star explosion... I guess Elon Musk is working on it.
The US spends about $600 billion annually on defense. Investing a few billion in reducing the risk of catastrophic climate change sounds quite reasonable, since trillions of dollars are at stake. Heck, even the "non-catastrophic" result of only a couple feet of sea level rise would swallow hundreds of billions of dollars of land value.
I'm not sure what rhetoric needs to be tuned down, since I have already read much of the literature from "minority researchers". I guess not the recent stuff, as I've gotten tired of it. As far as I can tell, the effort spent silencing scientists is mostly the exertion of fossil fuel companies. Who stands to profit from restrictions on fossil fuel consumption? I guess some renewable energy companies do, but few others in the short term. I have a hard time understanding the theory of a vast left-wing conspiracy to get us all to... what? Where's the motivation? It clearly is an ineffective technique to gain political power. Much more plausible is the idea of a few businesses trying to spread uncertainty. We saw that before, with cigarettes.
When you say, "listening to" do you mean believing the analysis of? It's funny you seem to hold PhDs in such high esteem. Almost everyone I know has a doctorate. Well, about half of them. And many of those in "hard science" or specifically environmental studies. I respect them, of course (since they're my friends), but I also think about their claims critically. Many of them need some coaching with statistics and non-linear dynamics, but hey, we can't all be experts on everything.