You are saying that once people reject empathy with animal suffering it is a slippery slope to rejecting empathy with human suffering by way of de-humanising certain groups of humans and treating the same as you would an animal. And I get the impression that you imply that working people embracing a sensitivity to animals on a larger scale would enhance human-human empathy on a larger scale.
Not exactly. Making working-class people (and anarcho-communists) face their desensitized apprehension of animals seems to me like a good first step in making them face their desensitized apprehension of other people, who could be their allies in the class struggle.
Now let's get back to Herr Himmler:
How can you find pleasure in shooting from behind cover at poor creatures [?] ... It's really pure murder. Nature is so marvelously beautiful, and every animal has a right to live.
Did he really have no empathy towards Jews and Gypsies? In fact, look at another of his quotes:
...It is one of those things which is easy to say. 'The Jewish race is to be exterminated,' says every party member. 'That's clear, it's part of our program, elimination of the Jews, extermination, right, we'll do it.' And then they all come along, the eighty million good Germans, and each one has his decent Jew. Of course the others are swine, but this one is a first-class Jew. Of all those who talk like this, not one has watched, not one has stood up to it. Most of you know what it means to see a hundred corpses lying together, five hundred, or a thousand. To have gone through this and yet - apart from a few exceptions, examples of human weakness - to have remained decent fellows, this is what has made us hard.
Himmler did have "empathy" towards Jews, as he'd expect anyone to have. But it was a kind of empathy that had to be fought against to do what is right. It is not that he had empathy for animals, but not for humans.
This does make me wonder, though. Maybe the word "empathy" isn't exactly what I mean as a positive necessity, here. Rightious indignation at hardships, perhaps? Something more moral than plainly immediate. I am unsure.
Then maybe I should just give up on working class lib, and focus on the more immediate and ever important goal of animal lib, right? 
Afterall, as soon as the animals are liberated, the workers liberation can't be to far off.
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Interesting food for thought (going along well with Himmler quote) - Hitler was a vegetarian.
We relate to animals in pain out of pity. what (I think) Lazy Riser was getting at was that this pitying-mindset seems pretty common amongst activist-types. This leads to Bono-Geldof "save little starving kids in Africa" stunts. Rather than relating to other people, and feeling solidarity, it becomes a power relationship based on pity.
The point is - I share common interests with, say, working class Iraqis, because I don't want the problems of wartime and because I know that we have shared interests. I can also relate to them. I don't pity them, I don't know any Iraqis, never been there. But I share common experience and common humanity and common interests with them. Thats human solidarity.
With animals its different. I pity them when they're being hurt - they're passive. I think it's too bad, all that unnecessary suffering. But I share no experiences, no interests, no nothing with them - we're different species, right? Most importantly, they are passive and powerless. Its up to our personal decisions what to do - its a one-way negotiation. That's why "animal rights" are a joke.