Under current regulations, we are not allowed the flesh itself on days of abstinence, but extracts from the flesh of animals, such as gelatin, clear broth, and rendered fat are allowed. Apparently, the change did have to do with the difficulty of knowing whether or not a particular product (such as margarine) had been manufactured using extracts from animals in it, and the desire of the bishops to remove scrupulosity with regards to the question.
If you are intent on avoiding products that have not touched meat whatsoever, for whatever personal reasons you may have (or because you’re cooking for a strict vegetarian or a vegan), look for kosher foods that are labelled parve or pareve. That means the product has not so much as touched meat or milk products. It may contain eggs or sea creatures that are kosher, since those aren’t fleishich (meat) under Jewish dietary law.
Kosher milk products are labelled Cholov Yisroel or Chalav Yisroel, and mean that it contains a milk product that has been supervised from the time of milking.
Just getting food that is kosher is not enough, of course, because Hebrew National beef franks are kosher!
Some foods are labelled vegan, too, which of course does not contain even eggs or seafood. Vegan cheeses are made using a starter not made from rennet, which comes from cows. So that can be a help.
It is important for us to avoid scrupulosity ourselves, but it is a work of charity to make allowances for others who have that weakness. (1 Cor. 10:23-33)