Sadiq, in a previous working life I did a lot of stuf with the food industry, at times in Muslim countries and learned a lot about this. Helal generally means nothing. What is the difference between a chicken that comes from a halal vs. a non halal chicken plant? ABSOLUTELY NONE, except the fact that in the halal one an imam takes a payment to produce a piece of paper "fatwa" which is posted near the door and near the machine that cuts the heads off the chicked there is a boombox (or other music system) playing a loop tape of Muslim prayers. Every now and then when the Imam needs some cash he'll insist on another inspection, which often consists of meeting the plant owner/manager to receive payment for another fatwa. We're talking about the modern world here and commercial food, convenience has voided whatever actual benefits of what comes from the halal process.

I've had vegetarian meals on United transcon and they've all been Muslim. One time I could see it particularly clearly when the family sitting next to me were Muslim and they were eating the same thing as me. Except they got lime pickles and yoghurt to soothe their curry. Inspired, I spooned the jam/jelly out of my yoghurt dessert on that occasion and used that instead.
I'm sure slashing the number of special meals they actually do offer also helps keep costs down. (A UA curry with pickle and yoghurt is actually quite nice, without it it's almost unpalatable)

Um, what's specifically considered animal fat, if not cheese, milk, butter?

No .... but use of meal preferences for feeding the CAPPSII engine (and results) has been tried. ;) (One "problem" was demographic data got "confusing" in that many muslims actually select "kosher" meals as a substitute out of concerns about just such haraSSSSment. Add in Soundex and other such nonsense, and more people get comingled. :) )

... that's not a wholly incorrect characterization (in that the "stereo" reciting certain words during industrial-level slaughter and "religious" persons wanting payment, etc.). However, there is a difference in preparation and content -- and at least there is supposed to be. For one, shellfish and certain other kind of seafood don't get mixed in and/or same utensils/dishes are not used in the preparation. For two, there is no "fatwa" involved. For three, at least with many of the vendors, there is an actual "manual" bleeding of the animal providing the meat.

You have to look REALLY carefully at a bag of sweets or a packet biscuits/cookies to make sure they haven't put some delicious beef lard or pork gelatine into the mix. Even an icecream or a milkshake might be thickened with some appetising animal carcass juice.
If you'd rather have just the milk then the fat is 'dairy'
If you're happy consuming whatever dribbles out of bones once they've been crushed and heated, then yes, enjoy a lovely glass of 'animal fat'.
With the way the meat industry operates in these times, you can expect a few more incidents of CJD or BSE - so be aware how wide spread the use of animal remains is, it's not just a hamburger that will maybe infect you.

Thanks to obscure food labelling, not eating pork or beef is harder than you might think.

Very correct. For those with a sweet tooth, gelatin(e) in candy may well be non-halal/non-kosher.

For further clarification: CJD, in effect, is what is popularly-termed as "mad cow disease".

What there is supposed to be, and what occurs are totally different and I welcome you to visit any industrial slaughterhouse operation in the mideast and see the "fatwa" (religious edict) prominently placed somewhere in the factory, Generally it says FATWA in the language of the country in use at the very top of the page. There is no manual bleeding involved. I take your point about the cutlery et al, but that is up to the airline, the point that I was trying to make is that if the airline has a totally seperate kitchen, etc, there is no guarantee that the whole process has ben carried out down the line, even if the basic food ingredients are "certified" as halal.

I visited industrial slaughterhouses in the Middle East (and elsewhere) over a decade ago. I did not notice signs in Arabic, Farsi, Urdu, or English saying "fatwa", but I did notice certificates from some government agency or religious institution/agency seemed to be in the management's office and/or near the loading/unloading docks indicating that the products were halal.

What occurs and is supposed to occur is apparently in the mind of the beholder. That much was apparent to me too -- given the variations between abattoirs for even the same caterer/supplier in the same country or from country to country.