@Pokari
That's actually a pretty involved issue and people have debated that for some time. Let's take one extreme. Not feeding a stray cat and risking that it might starve to death may seem cruel and heartless, but consider the misery that single cat might go through may be amplified by many more if that cat somehow manages to have kittens. A cat can have kitten as early as 18 weeks or so and have 2 to 3 litters a year. And every single one of those kittens will go through similar hardships. Feral cat population absolutely EXPLODE where they have resources which includes abundant wildlife AND people willing to feed them.
Secondly, generally speaking, cats are capable to providing for themselves, especially if they're fully feral. In fact, maybe a little too much so. You mentioned the devastating effects they can have on local wildlife, especially song birds. Feeding them may simply allow the ones who would not have made it naturally to thrive and contribute to the overpopulation and problem as well as the depredation problem, because even the indoor cats that gets fed regularly do hunt and kill (but maybe not eat) local wildlife.
Third, and perhaps, paradoxically, just feeding them isn't enough. There are health issues that the cats can have living in the wild that feeding them will not solve. In fact, by the effect of convenient feeding, it may allow the weak and diseased ones to keep living and transmit what they have to otherwise healthy and capable feral cats.
So usually, the most good feeding feral cats does is to your feeling. It makes you feel warm and fuzzy and makes you think you've done something when it's, at best, neutral. Which doesn't make it bad, necessarily, but in a case like this, when you have in effect supported a cat, you shoulder on additional responsibility. That's why Tsubaki was so mad when Himari became indecisive about the kitten. That small life was a direct result of Himari's capricious charity that was more for her own warm and fuzzies than for the cat. If you recall, before that, Tsubaki wasn't mad; she simply told Himari that she shouldn't feed a stray, which is a valid, if in debate, opinion among those in the rescue circle.
You mentioned poor people, and at least in the case of homeless, it's acknowledged that simply giving them money doesn't help. There's a reason why they're homeless and money you give them now will disappear just as quickly as the money they had before. And there's a healthcare parallel as well, as many homeless have either substance abuse and/or mental health issues that a direct charity does nothing to address. It's not that you shouldn't give them money (which I think is more for your warm and fuzzies than actually helping) but the resources should be directed in other ways.
And it's the same here. Helping stray isn't about just feeding them. It's a band-aid over a wound that might provide a temporary relief but the wound itself might fester and rot later. Many rescue organizations will neuter/spay and release. That breaks the reproduction cycle. Some will even trap and euthanize, although support for that is really low.
Anyway, I don't think the manga's position on feeding stray is evil. It's just that you shouldn't do it. Which may seem heartless, but it is one of the major positions among rescue circles. It makes a further point that if you do feed them, then you have voluntarily shouldered on additional responsibility and you should follow through. Which again is a common position among the rescue circles.
As for her disillusionment with her volunteering, that's also incredibly common. Volunteer groups tend to be led by one or two very committed core who aren't discouraged by ANYTHING and then others who come in with all the enthusiasm in the world, bright-eyed and bushy-tailed, and then get battered by the reality. In this manga, it seems that Tsubaki saw that she was being used as a convenient excuse for people to abandon kittens without feeling guilty. That would crush anyone's enthusiasm. Some volunteers can pick up the pieces and move on, but others can't, and I don't think you can blame them. It's brutal. I've personally seen people coming to animal shelters thinking they'll get to play with puppies and kittens all day long and then get ground down to dust by how it actually is. How do you tell a volunteer that there is a parvo outbreak and you can either spend the budget for the rest of the year to treat the puppies, or euthanize them, sanitize the facility, and try to help the batch that will come in next week? If anything, that dynamic makes this manga seem more real to me, as if the mangaka had actual experience in volunteering at a similar organization.