Yes and no. I dont think Lisa’s enthusiasm for animal rights is unnatural. Lots of people have that kind of enthusiasm (craziness) for something or someone.
When choosing animal rights as Lisa’s “thing”, the writers of The Simpsons has made it possible to have Lisa care about almost all issues concerning environmental problems on the entire planet.
This opening enormous possibilities for satire and subtle criticism of our society today.  Just look at the interactions we have seen between Lisa and Mr. Burns.
Burns thinks: I don’t care; I want to make money now.
Lisa thinks: I want a better world tomorrow. 
I agrea that this issue can be pushed to far sometimes.  But then Lisa is the right person in the show to do it. She is still only 8 years old. And it is accepted that he dreams is not hampered by such thing as what is politically and economically possible.

This was meant in a more general sense. That Lisa is a person who “burns” for a cause. That is a Danish expression. In Denmark she would also be called a “fire soul”

*sighs*
It's a tough question.
I always though that being so intelligent Lisa could find a better way to care for animals. I always mention that scene from 18x05 with a bucket of red paint. Her actions only led Krusty to wear more fur and it seemed that she did that childishly and without much thinking. Also, a moment Dag had mentioned. She gathered all animals she could find in town without thinking, how would she feed them. They could be killed.
So, yeah, I suppose she is exaggerating very often. But still it's better than if she was cruel careless girl and I think one day it'll be possible to her to solve all problems staying calm and competent.

Okay... I'll chip in here.

In my opinion, Lisa takes animal rights way too seriously. Yes animals are living creatures and are entitled to humane treatment, but sometimes the degree to which she advocates animal rights is ridiculous. She seems to think that she knows exactly what the animal wants, as if she can talk to it or read its mind. Well none of us are telepaths; she could be fighting to release an animal from a life that it actually enjoys.

Take PETA for example (since Lisa is a member, according to one of the more recent episodes) - they believe that ANY form of animal ownership is enslavement, and that the animal is unhappy about where it is at. They think that by granting animals "freedom", they'll be improving their lives. What sickens me the most is that they actually try to compare some of their methods, and their message, to the emancipation of the slaves during the Civil War (in America of course).

Animals aren't exactly living it up when they're in the wilds. It's a harsh fight for survival out there. My point here is that it's not really wise to believe that you understand what an animal wants, and make decisions for it. You could be very wrong. I'm sure that household pets that are treated with love and care (for example, my cats) enjoy their lives very much, and would be perfectly content to live out their days with their owners. Companionship and love can make an animal very happy and healthy.

Anyway, that was sort of an off-topic rant, but it conveys to some degree how I feel about PETA's attempts to "free" animals (sorry, Paul). I think that Lisa is being overly-liberal in her convictions about animal rights, and should learn to back off and consider other viewpoints.

Yggdrasill
It's not even a "problem" in my opinion. Animal activists make it out to be this great injustice, but really, the only crime is when an animal is abused. There's nothing wrong with owning a pet, even in my opinion eating meat or animal products. Giving up drinking milk especially... that's really extreme. I don't see how drinking a cow's milk is hurting a cow in any way.

People are just looking for something to make a fuss about. And since animals "can't speak for themselves", and are "used by humans for clothing and food", it attracts radicals who want to fight for a cause. Well go ahead and fight for your cause, but to me, you're just wasting your time. People need protein and nourishment, so they eat meat. People need clothing to cover their bodies, so they'll wear wool or fur or leather. It's not murder; it's survival.

Dagdamor
Well, vegans say that on farms where milk/wool/eggs are produced, animals live in so bad conditions, that they life is a non-stop torture, that they suffer from thirst and hurt by very-very small and uncomfortable cages and they almost can't move during whole their lives.
The same time antivegans say, that while you hurt few animals making one fur coat, the process of making artificial materials includes many very pollutng stages and lead to much more animal deaths.

That's all is very complex bullshit

Well I can say from experience that the life of a dairy cow certainly isn't non-stop torture (and no I'm not a dairy cow...).   Cows are not kept in cages, in fact on most dairy farms, they'll spend most of their time outside grazing during the spring and summer.   On some farms where the climate permits, they'll be out most of the year.   Likewise, you won't find many sheep that are housed, except for ewes during lambing and again, the rest of the time they'll be out.   There are welfare concerns over battery cage systems for egg production.   I don't personally like to see hens caged but I can guarantee they won't be suffering from thirst.   The last thing a farmer wants is to keep livestock under conditions that will cause stress not just for the sake of welfare but also for the very practical reason that a stressed animal won't be as productive.   I can't comment on the situation worldwide but in the UK and Europe, the legislation that governs farm animal welfare is very strict.
Anyway, just a little off-topic there...