That supremely depends upon what you define as “fundamental” and in what context. :)
Do some ideas have higher leverage than other ideas: certainly. Is it easy to tell a priori which ideas those are: not entirely.
Consider log-structured merge trees (LSMs) were invented in 1996; Amazon S3 was released in 2006. Some might consider these fundamental ideas that have existed for 28 and 18 years, respectively. Have you mastered these ideas enough to understand how the cost structure of S3 enables you to implement a really economical distributed LSM at extremely low cost because S3 doesn’t charge you for bandwidth usage?
For sure, but I think even if you didn't consider those particular examples to be a part of the fundamentals, if you had a solid command of basic algorithms and data structures (e.g., including your basic trees, including B-trees) and some basic math, you could easily pick up LSMs and figure out how to exploit the S3 cost structure as needed.
The point of the fundamentals as commonly construed is to allow you to quickly pick up novel concepts as needed as they're almost always a slight extension of the fundamentals.
I would say focus on what's fundamental and pragmatic to each (e.g. immediately relevant). All the recent stuff actually isn't that, unless you're the one doing the research or implementing them. I think LSMs are great and I'd gladly use a db that uses them but I don't need to know how they work, only their properties when selecting a db. If I'm using a relational DB though I'd damn-well better know how indexes work.
Do some ideas have higher leverage than other ideas: certainly. Is it easy to tell a priori which ideas those are: not entirely.
Consider log-structured merge trees (LSMs) were invented in 1996; Amazon S3 was released in 2006. Some might consider these fundamental ideas that have existed for 28 and 18 years, respectively. Have you mastered these ideas enough to understand how the cost structure of S3 enables you to implement a really economical distributed LSM at extremely low cost because S3 doesn’t charge you for bandwidth usage?