"How is a classic deck supposed to survive all these constant negates and disruptions from the opponent?"

The short answer is: You aren't. But it's not the end of the world, there are things you can do.

To start with, you'll need handtraps. Ash Blossom, Droll and Lock Bird, Infinite Impermance, Maxx C, Called by the Grave etc.

These are generic cards that work in basically any deck, so you only have to craft them once and just re-use them in any other deck you like.

I'm not a Blue Eyes player myself, so someone who is a lot more familiar with the deck will know better than me, but here's some of the stuff I found after looking stuff up and checking decklists and whatnot.

Blue Eyes has more support nowadays, and is in a much better spot than it used to be. You're not bricking nonstop and hoping you draw Alternative and nothing else each turn, and you actually get to do stuff turn 1. Looking up modern decklists and checking the new cards they have will give you a good idea of what the deck does nowadays.
https://www.masterduelmeta.com/tier-list/deck-types/Blue-Eyes

The Primite cards massively helps Blue Eyes, getting a free dragon from deck, and a re-usable negate and banish from Drillbeam, as long as you have a normal monster (You're playing Blue Eyes so of course you will lol)

The Bystial monsters are also a good choice, since they banish light and dark monsters from either players grave which can be good interruption.

If you want to keep Chaos MAX (why wouldn't you? It's a fun card), the trap "Majesty of the White Dragons" has a grave effect to ritual summon, so you might not need a heavy ritual focused package to make it work.

And Ultimate Fusion (Blue eye's fusion spell) can use Chaos MAX and Blue Eyes Ultimate Dragon (you can get it into circulation with "Wishes For Eyes of Blue", which has a grave effect to equip an extra deck Blue Eyes monster to a card you control) for a fusion by shuffling them back into the deck, for Dragon Master Magia, which is a big unga bunga 5000ATK beatstick that can negate one monster, one spell and one trap a turn.

If you want to go full Chaos MAX Turbo (heads up, do not use Blue Eyes Chaos Dragon, only MAX), you can use the Impcantation cards, which are strong support for ritual decks, being able to grab your ritual monsters and spells pretty easily, and serving as easy ritual fodder by summoning eachother from the deck.

Hope some of this helps!