As I raised in a more recent one of these threads, the Ashkenazim used "Schmaltz" for cooking, which was either rendered duck or chicken fat. Given Chicken are about as easy to raise as pigs, I don't see why this wouldn't be a valid replacement for lard in cooking for Northern European Muslims.
Quantity. You can get fat out of a lot of domestic animals (sheep are very good, if you have the right breed), but pigs give you the best output. You can't raise chickens on beechnuts and acorns, or herd them in the forest, so poultry fat will always be in somewhat limited supply compared to pig fat.
In Central Asia people used fat-tailed sheep to produce animal fat which was abourt equally important in cooking as pig fat in Northern Europe, so it's doable, but it would require a big shift in agricultural patterns. The problem isn't that you can't do it, it's that at this point a system has emerged in Europe that has pig-raising as a core source of animal protein and fat. These things take a long time to change. And you have to keep in mind that these European Muslims aren't going to be caricature Wahhabis chopping off your head if you so much as taste bacon. I suspect the idseaof eating less meat to reduce the ecological footprint is a reasonable enough analogy - how long till it makes a dent in America's cattle industry?