1. For one thing, what exactly is "Judaism" as a culture? I think of it as a religion, and since it is an anachronistic religion (from a Christian perspective) then why would anyone in Europe who is interested in preserving a Christian culture go out and convert to Judaism?
2. As others have pointed out, you are making a gross assumption that Christian nations have an inevitable death wish that results in their decline. I'd also point out that many Europeans are perfectly OK with their culture (however they define that) dying -- as long as they don't have any discomfort and difficulty while it happens. If anything, I'd suggest that Israel is almost identical to Europe in its secular, leftist mindset.
3. What is the ultimate end of science, in today's world?
As I said, anyone who converts to any religion for some lowly pragmatic, utilitarian purpose (such as to "preserve a culture") is doing it for the wrong reason. Obviously if one's purpose is to preserve a chrstian culture, converting to Judaism (or Noachism) would be self-defeating.
However--if one is looking for the Truth then investigating the claims of Judaism makes perfect sense, and why no one ever seems to think of this absolutely eludes me.
Fortunately, being from the Bible Belt, the only (lehavdil!) "chrstendom" I ever knew was Saul, David, and Solomon. Us Bible-thumpers are notoriously unappreciative of the thoroughly alien (to us) medieval European civilization--thank G-d!