Any discussion about this is going to be highly dependent on local conditions. But having said that: my house is in a rural area delightfully flooded with birds, with a variety of bird feeders I put out and insects I try to support, and a number of indoor/outdoor hunting cats, and there are plenty of tools to keep cat birding down to darn near zero. The basic thing to reason about is how cats hunt and birds feed. Cats need to sneak close, then ambush in a burst of speed. Birds though have extremely fast reaction time and of course can go straight up. They don't need much. Cats also have limited ability to jump, and will go after other easier creatures most of the time if they can.

So first, basic obstructions nearby the house/barn are kept low. I have some former field I've mowed down into lawn (full of whatever random stuff is around), there are some trees and rocks around, and that's it. There is plenty of field/woods full of approximately 12.45 billion chipmunks, mice and voles by my rough estimate, but small birds don't tend to ground feed there they and in brush off the ground. Cats can't sneak up well anywhere in the vicinity of feeders.

I have the feeders themselves suspended off the ground with ropes between trees/buildings and a second rope going to pulleys so I can lower them for refilling and cleaning. The feeder bottoms are at least 9-11' off the ground and 10' from the nearest structure or tree. This renders them effectively invulnerable not merely to cats but conveniently squirrels, raccoons, and black bears. With some platforms mixed in, even ground feeders can get some aerial action.

But most do want to be on the ground, and there all it takes is a small low wire fence. And by low I mean low, like a foot or two high maybe. It looks fine in the lawn and is easy to move, it's trivial to step over or for cats to hop over. But by forcing them to jump it destroys any last potential ambush or sprint. In the time they go vertical no bird will miss them and they lose speed. Even though cats can get over without the slightest difficulty it's amazing how they instantly don't even bother, guess they reason out right away that if they have to leap into the air well before their target it's pointless to even try. They don't stalk birds at all at this point just wander by.

The only remaining threat is bird strikes on windows. Cats figure out that noise pretty fast and will go to investigate if they're in the area (which they often aren't granted). No perfectly solution there except to aim to reduce bird strikes which is a good goal anyway. I use a mix of screens and stickers. Window screens as well as their core function of keeping out insects while letting in air are excellent shock absorbers and reflection disrupters for birds. The normal downside is they do interfere with views (and the enjoyment of bird watching to some extent), but high density enhanced visibility screens like UltraVue/BetterVue can help lesson that tradeoff. For windows where screens aren't doable or truly are undesirable (particularly in winter) I use WindowAlert stickers. They actually blend pretty well with windows, being fairly translucent in visible light, but reflect very strong in UV which most birds (particularly song birds) can see but we cannot. They're chemical so they have to be replaced every 4-6 months but are quite effective. I also use some regular visible stickers that simulate spider webs which birds instinctively avoid.

A bit of thought and effort and you can have quite a lot of wildlife living together reasonably well, and that includes a good number of feline friends. Totally natural lawn field, seeding some wildflower meadows, decent varieties of flora with no poisons, carpenter bee houses and so on can all give insects a boost too.