How does the meat in Weisswurst get so white?
The real question should be "what makes sausages pink" - but more later.

All meat turns greyish-white or brown when cooked. This is due to the myoglobin, which makes raw meat look pink or red, being not heat stable. When cooked it denaturates to metmyoglobin, which is grey-brown. 

For pinkish sausages, curing salts are used. They contain sodium nitrite, which transforms the myoglobin to a more stable form nitrosomyoglobin, that becomes Nitrosomyochromogen when heated - and is red.

For Weisswurst, simple table salt is used in a sausage mixture that contains light coloured meats (veal, sometimes pork), fat and water, hence the whiteish-grey colour. Curing salts have a preserving effect that simple table salt does not have. Traditionally, Weisswurst was therefore supposed to eaten before noon. Modern refrigerators have made this former necessity obsolete, yet the custom remains.