My baby comment was mostly tongue in cheek but the part that was serious is more about why animals are excluded than why children are included.

What's so terrible about a well-trained, well-behaved animal inside a restaurant or grocery store? How is it worse than having a well-trained, well-behaved toddler inside a restaurant or grocery store? Just what is it that these health regulations prohibiting animals are protecting us from? How is a dog in a restaurant more of a threat to my health and safety than the same dog in a park?

My kid takes a bath every day.  How often do you wash your dog, chinchilla, cat, or other pet?

Thalia

Since neither your kid nor my dog, chinchilla, cat, or other pet will be handling or serving food to other customers, I fail to see your point.

If a baby shits it's diaper at the table beside me when I'm trying to eat, I don't think I'm going to say "at least he/she was bathed today".
I'm just going to lose my appetite.

Just sayin'.

What's so terrible about a well-trained, well-behaved animal inside a restaurant or grocery store? How is it worse than having a well-trained, well-behaved toddler inside a restaurant or grocery store? Just what is it that these health regulations prohibiting animals are protecting us from?

I believe that one of the reasons is that many people are allergic to animal dander, and in environments such as diners or whatever, where people are seated fairly close to one another that closeness may trigger an allergic reaction. I also believe that the possibility of fleas, ticks and/or other parasites being carried by pets into eateries is another strike against them.
On a personal note, we've had our greyhound into quite a few bars where food was served, but have yet to be allowed* inside a restaurant with said hound - although if there's an outside dining area attached to those places, we've generally been welcome to dine there.

*  we really don't try to get into restaurants with a dog in tow; mostly if we're out and about with our dog and happen across an interesting place while we're hungry, we'll ask if he's allowed in - mainly out of curiousity 'cuz we certainly don't expect access to the inner sanctum with its patrons, most of whom may not appreciate 98lbs of greyhound eyeballing their food :-)

Somewhere in my soul, there's always Rock -n- Roll... Joe Strummer

I believe that one of the reasons is that many people are allergic to animal dander, and in environments such as diners or whatever, where people are seated fairly close to one another that closeness may trigger an allergic reaction. I also believe that the possibility of fleas, ticks and/or other parasites being carried by pets into eateries is another strike against them.

Airlines allow people to bring pets into the cabin and that's a much more confined space than a restaurant. People are allergic to peanuts, but restaurants and grocery stores aren't prohibited from serving or selling them.

People carry parasites, too. Between flea collars and Frontline I'd think restaurant patrons would be more at risk of getting head lice from a human than getting fleas or ticks from a dog.

In restaurants, at times, if there is a crying or smelly baby nearby, you could ask the waitress or maitre d politely if you could move to a different table.

Why is the onus on the person who is being decibel-ed or crappy-diaper-ed out of their paid for recreational culinary experience to be relocated and not the decibel-er or gas-er?   Babies, as you noted, do have rights as human beings, but they are also not of the age of majority and therefore any disruptive effects that they may have on the environment around them falls on the shoulders of their tenders.  Or put another way: when I have the "right" to walk into the restaurant of my choice:

1 - carrying a boom-box with the soundtrack of my choice (including one of a screaming baby) and not be ejected; or

2 - dressed in overtly and wide-ranging smelly clothes including soaking in my own urine and/or feces and not be denied service;

Then babies have the same "right".  Hey, you said "rights" - that means we all have them.  "Rights" are something possessed by all of us, correct?  If you don't agree that I have the same "right" to disrupt a public space in a similar fashion, then I suggest you drop this talk of "rights" and re-phrase it as "It's my personal belief that people with babies are to be allowed an unofficial yet theoretically socially sanctioned pass w/r/t what is acceptable behavior in a public space.  Because until I can do the same thing, it is not a "right".  

That said, babies and monkeys are not to be put in the same category and this woman should get over herself.  I fully agree with that.

And other lampoonery of such kind.

Tyger, what you are overlooking here are what we call manners.  Being socially polite when you are in a social context is the correct behavior and there should be an onus for people to try and be non-disruptive if possible.  In all honesty, anybody can be offended or uncomfortable in any restaurant for any reason.  You should take ownership of your own special needs.  In a family restaurant, you should expect families, children who can be loud or disruptive.  It is also reasonable to expect the parents of the loud disruptive or dirty diapered kids to do their best to mitigate some of the discomforts they cause other patrons.  

But in the case that you can't stomach being near someone's kids, propriety suggests that you seek to be moved to another table or leave the restaurant.  

Be honest Tyger, have you ever been in a restaurant with smelly diapered children (and or adults) and had to deal with loud and disruptive behavior ruining your dining experience?  If you have, then how did you react?  Did you ask for the family to be removed from the restaurant?  Did you confront the offending people?  Did you file a complaint?  I want to know how you reacted in such a circumstance.  Do you wish children to not be allowed in restaurants?:  Special needs citizens?  The elderly?  How much can you take?  

Unfortunately, when you go out to a restaurant, you are not guaranteed a wonderful experience.  You could get bad food, bad service a bad environment, poor cmpany, and less than tasteful social experience.  One of the things we do in open society is accept a few of these imperfections and try and make the best of it.  

Once I took my family to the 99 Restaurant.  My son actually got sick and vomited on the bench and floor.  It was embarrassing, we didn't realize he wasn't feeling well.  None of the people sitting near us seemed to complain, and the staff was extremely helpful to us in a difficult situation.  My son was 4 at the time.  The 99 Restaurant is a family restaurant, and sometimes you gotta expect unpleasant occurrences.  That being said, I wouldn't want pets and monkeys in the restaurant.

1 - carrying a boom-box with the soundtrack of my choice (including one of a screaming baby) and not be ejected;

Well, a boom-box is not equivilent to a crying baby.  Do you have the right in a restaurant to talk loudly?  Or even laugh raucously?  I'd suspect you do, though you might be asked to tone it down.  Similarly a family with a baby that is continuously crying should be asked to take the baby either to a restroom or outside till it calms down.  And honestly, how often do you encounter babies that cry continuously?  When my children were babies, we often took them to restaurants and I can't remember a single case of them crying for long periods of time.  Whenever they cried, my wife and I took care of it by dealing with whatever was making them cry or removing them from the area if we couldn't pacify them in a reasonable amount of time.

2 - dressed in overtly and wide-ranging smelly clothes including soaking in my own urine and/or feces and not be denied service;

I certainly wouldn't deny you service if you accidently soiled your clothing, as long as you went to the restroom, cleaned yourself up, changed your clothes and either discarded your soiled clothes or securely bagged them up so that the smell was not obvious to those sitting next to you.  Which is what parents should do if their baby soils its clothes.

In your comment you criticised babies, but your ire if focused on the wrong party.  Your ire should be directed at parents who fail to take care of their babies.  BAbies are for the most part helpless and unaware of their effect on those around them.  It is the responsibility of the parent see that their baby's behavior/aroma is not disruptive of the people around them.

"a boom-box is not equivilent to a crying baby"

No joke. Unlike with a boom box, it's really, really, hard to break dance to the sounds coming out of a crying baby. I learned that the hard way at a battle.

I don't think mental midgets are as calming as monkeys.  

They are if they can dance.

It's the end of the world as we know it, and I feel fine