I have a completely different perspective on this issue to everyone who has posted so far. There's a bit of background to explain why I think this way, I'll try to be brief. But in being brief I run the risk of giving the wrong impression. So, if anything I am about to say sounds blasphemous, or insulting to God, or a promotion of Islam, or anything of that nature, you've misunderstood me...
This thread is about meat offered to idols. The example being used is Halal meat. I do not believe this is an example of meat offered to an idol. If anything, it's the exact opposite - halal meat by definition has NOT been offered to an idol. That is a controversial statement that will need some explanation...
I do not believe Muslims worship a demon named Allah. The word "Allah" is simply the Arabic version of the Hebrew "Elohim" (note the "al" / "el" at the start), and is equivalent to the English word "God". Arabic Christians were calling God "Allah" long before Mohammad was born, and still call Him "Allah" today. Muslims ATTEMPT (please note the stress on that word) to worship the God of Abraham, the Creator. There is only one God of Abraham. There is only one Creator. He is YHWH, the one true God. However, Muslims have been taught many lies about who He is and what He wants them to do.
To put it another way - Jews attempt to follow the God of Abraham, but have incomplete understanding of Him as they reject His Messiah, so fail to follow Him correctly. Muslims, Mormons and other such cults also attempt to follow the God of Abraham, and accept His Messiah at least partially (as a prophet), but have been seduced by false prophets and doctrines of demons, to believe lies, and therefore also do not follow Him correctly. When a Muslim says "Allah says we must do X", he does not mean "a false god says we must do X", but rather "I believe that the God of Abraham says we must do X (but I don't realise that I'm actually wrong about that...)". When he prays to "Allah", he is not intentionally praying to a demon, but rather is genuinely trying to pray to the God of Abraham - whose commands he unfortunately severely misunderstands, and demons may certainly be whispering to him and be pretending to be the voice of God responding to his prayer.
Another way of looking at it: Say I tell my daughter to tell my son "Dad says take your dirty washing to the laundry", and she actually tells him "Dad says to burn your dirty washing", and my son responds by burning his washing. When asked why he is doing something so ridiculous, he says adamantly "Dad commanded me to burn my washing, and I am doing what he said". Is my son choosing to not obey Dad, but rather obey some false dad (let's call him "Evil Dad")? Of course not. Rather, he's genuinely trying to obey his dad - but is the victim of a lie. He should have looked into the truth of the instruction better of course, he's arguably being foolish - but even that doesn't change the fact that he genuinely believes he is obeying his dad.
Allah isn't an idol. Allah simply means "God". But many people think very wrong things about God, as we all know well...
So, what is Halal? Halal simply means "acceptable", like kosher. Most food, by definition, is halal. A food can be both halal and kosher simultaneously - fresh vegetables for instance are acceptable to both Muslims and Jews so are both halal and kosher.
Although Muslims have an enormous amount wrong, when it comes to meat they basically believe a simplified version of Torah. Don't eat pork, don't eat blood, don't eat meat offered to idols. They are very strong on not eating meat offered to idols - that's why fanatical Muslims go around blowing up anything that even looks like an idol... To make sure they never eat such meat, a Muslim is only allowed to eat meat that has been slaughtered by a Muslim, a Christian, or a Jew - because such believers would never offer their meat to an idol, but only to the God of Abraham. Meat that has been slaughtered by a Muslim, Christian or Jew is therefore "halal" - acceptable for Muslims to eat.
This means that if any of you kill and eat your own mutton / goat / beef (provided you drained the blood), you're eating halal meat. Meat that a Muslim visitor would be happy to accept as acceptable, because it was slaughtered by a Christian.
Now when a Muslim slaughters an animal, they are supposed to do a couple of very minor things - pray thanking God for the animal (which most of us would probably do also in some form, not legalistically but just through gratitude), and kill the animal facing Mecca (which is only natural since they always pray facing Mecca, so if they're praying when they kill the animal they'll be facing that direction anyway). This is simply expressing gratitude to the God of Abraham for providing the meat, in the particular way that Muslims act when they pray.
Throughout most of history, a Muslim would get "halal" (acceptable) meat by simply going to their nearest Muslim, Christian or Jewish butcher, buying meat, and they'd know it was not offered to idols and therefore acceptable to eat. However in these days of global trade, you don't know who actually killed the animal you buy, and for all you know it might have been someone who truly does worship idols, such as a Hindu. So some groups of imams have set themselves up as halal certification authorities, and go and inspect meatworks and other food production facilities and certify whether they are acceptable for Muslims given their own particular understanding of the rules, and have copyrighted "halal" logos that they allow particular businesses to use to demonstrate compliance. As happens with religious people, the rules of a particular certification board might actually be more restrictive than the bare minimum outlined above - for instance they may only accept Muslim slaughtermen. But the "halal" label does not mean the food has been offered to an idol - rather it still just means the food is "acceptable" for a Muslim according to the view of a few individuals.
New Zealand produces massive quantities of beef and mutton, and over 90% is exported to dozens of countries, many being Muslim. To simplify processing, every cattle beast or sheep killed for export in NZ is halal slaughtered. Then meat going to Malaysia gets a halal sticker, meat going to the USA does not, depending on what will sell better in that particular market, but it's all the same meat... In practice, as I understand it, "halal slaughter" here simply means that there's a person who's done a brief certificate of study in halal slaughter techniques slitting the throats of the still animals after they've been electrically stunned, while pretending to pray. In practice, there are two praying people, so they don't get bored and forget to pray or tired and do a poor job, so one works inside while pretending to pray while his mate stands around outside having a smoke, then they swap places for a while... It's considered the easiest job in the meatworks, basically a joke job, just a box-ticking exercise to allow export into large Asian and Middle Eastern markets.
Is such meat acceptable to Christians? I'll jump back to the illustration of my clothes-burning son for a bit. Now, let's say this son goes to the pantry, gets out a cake, calls out "Thanks Dad for making the cake", and then goes to share the cake with his siblings. Should his siblings say "He didn't really thank Dad, because he doesn't follow Dad, he actually follows Evil Dad. So when he said "Dad", he must have actually meant "Evil Dad". So he gave Evil Dad the credit for making the cake, not Dad. We can't take this cake, because Evil Dad's been given the credit for it and not Dad, so it's been defiled and we have to refuse it.". Ponder it for a bit, because that seems a bit ridiculous, but it truly does parallel the situation we're discussing here where a Muslim thanks "Allah" for meat and then Christians say "well he doesn't really mean Elohim because he actually serves Evil Elohim / Evil Allah...".
I have no problem eating halal meat.
In fact, if you want to avoid pork, the simplest way in most of the world is to eat halal! America is very unusual in having a large Jewish population so kosher food is actually available. I've never seen a kosher label in my life, but see halal labels everywhere in the supermarket. So if for instance I wanted to only buy sweets made using non-pork gelatin, I'd look for the halal label and buy those ones - and if I were to look up local Jewish lists of acceptable food items I'd find that exactly the same items were listed as kosher. Because halal doesn't mean "offered to an idol". It just means "accepable".
On the other hand, if I were to be offered meat off the altar of a pagan idol, then I'd have to refuse for the sake of others conscience, as outlined by Paul.
Remember what I said at the start - if you think I'm promoting Islam you've completely misunderstood me, Islam's evil.