But do we (i.e. the human race in general) have any more skepticism about such claims than we used to? Most people still do believe in religions that include some form of eschatology.

It might just be that scientific talk about existential risk seems like a competing meme to religious people (you're not allowed to believe in something that says the world won't end the way your religion says it will), while non-religious people may tend to see discussion of global catastrophe as in the genre of apocalyptic religion.

(Then again, global warming doesn't seem to have that problem, so maybe it's just a marketing issue...)