Generally such health fears will be to do with the amount of additives in "processed meat". The use of Mechanically Reclaimed Meat (MRM) is also rather frowned upon.
At the height of the media coverage of such issues in the UK, Turkey Twizzlers were singled out for particular hatred, the ingredients list almost speaks for itself. (Via: http://www.guardian.co.uk/media/2005/mar/23/broadcasting1)
Turkey (34%), Water, Pork fat, Rusk,
Coating (sugar, rusk, tomato powder,
wheat starch, dextrose, salt, wheat
flour, potassium chloride,
hydrogenated vegetable oil, citric
acid, spices, onion powder, malt
extract, smoke flavourings, garlic
powder, colour [E160c], mustard flour,
permitted sweetener [E951], herb,
spice extracts, herb extracts),
Vegetable oil, Turkey skin, Salt,
Wheat flour, Dextrose, Stabiliser
(E450), Mustard, Yeast extract,
Antioxidants (E304, E307, E330, E300),
Herb extract, Spice extract, Colour
Note the percentage Turkey in that list, and that is MRM. Turkey skin is added separately in to the mix as well you will notice, as well as pork fat.
Sausages can fall in to this trap, many cheap sausages are around 30-40% meat and contain a great deal of additives. There are however many good quality sausages that contain few, if any, additives. Some people advocate that sausages should be close to 100% meat, personally I think they are better with a good bit of rusk and other ingredients.
It is the word processed that is key to the argument. Sausages are necessarily "processed" meat, in that the meat is not in its original form. But the health issues are for when "processed" means a lot of unhealthy additions, poor quality meat, a great deal of fat, salt, etc.