Well if the Ancients were anything like the Old Ones of Warhammer Fantasy, they weren't in to chaos at all, and were rather very ordered.
It was the war with the Necrons, that led to them uplifting many new races and gifting them with powerful psyches, that let to all the turbulence in the warp and the coming of the Chaos Gods.
Also, the Warp doesn't really have an underlying effect on everything. Most inanimate objects and nonsentient animals don't even register as a blip in the Warp, with just as little (if not less) flowing the other way. That's what makes Psykers so special, they're a great big conduit for power that would otherwise have little to no access to the material universe, outside of areas where the two overlap, like the Eye of Terror.
So Chaos isn't playing hell with crystals, or the evolution of lifeforms, and so on. You won't just land on an unexplored planet and find places where the warp leaks in to reality, without someone (something) having done something to put it there. Even if it's just from the raw malevolent intelligence of some being or another.