That depends entirely on you as a person and how symmetrical you need your rules to be.
As they say in the playtest... the Custom Backgrounds right now are two skills, a tool, a language, a Level 1 feat, and 50 GP of equipment. Which means that if someone decided to use a Background from the 2014 book for whatever reason... it won't be "equal" to a 2024 Background in terms of "stuff".
This may bother you. This may not. How in-depth is your particular game's balance? Will a character built with the 2014 Background that doesn't have a Level 1 feat now become massively underpowered because they don't have it? Or is your game more open in terms of mechanics and balance and you realize that a PC without one of these feats will barely notice it?
It'll be the same way I'm sure with the eventual Class and Sub-Class playtest documents. There will be some people who will compare and contrast every single 2014 and 2024 counterpart and declare that the new stuff is in no way backwards compatible because their game's balance is on such a razor's edge that any slight boost that 2024 classes may have over the 2014 ones will screw things up in their game entirely and thus every single character thing they bought from the 2014 PHB, Xanathar's and Tasha's are now completely worthless. Whereas other people will look at the 2014 and 2024 Bards (for example) and know that they could use either one or both in their game and not a single thing will cause issue.
So take a good long look at your own game and how you run it and what facets do you put under the microscope for balance reasons (if any). That'll give you a better idea of what parts of the 2024 books might be things you'll need to look at if you decide to buy them, or convince you not to buy them and just continue to use what you already own.
Why would you discard any books?I admit I am more than a little confused about the changes and what ‘backward compatible’ really means. So what books are keepers and which one are not? So will Tasha’s work with the new edition? What about Monsters of the Multiverse? Even Fizbans? The only thing I think I know is the MM and PHB are out/ being replaced and old adventures remain useable. The rest is a big mess to me.
I mean, I'm with you 100%. But I also cannot deny that there are players here on the boards that really seem to notice even the slightest differentials in game balance based upon how they play their games.Honestly, I feel like the people who are worried about "balance" between a 2014 character and a 2024 character have never played a game with a party of "regular" 5e characters and one built by an optimizer. Barring a 2014/24 hybrid-character built by a min-maxer, I suspect that a "regular" 2014 character and a "regular" 2024 character will be nearly indistinguishable power-wise.
That was my mentality too for a long time. I had an amazing collection of 1st and 2nd edition books. But my wife eventually told me that stacks of books around the house, numbering in the hundreds, not to mention miniatures, was not how she imagined our home decor when we marriedWhy would you discard any books?

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.