White wines have just as much or more sulfite than red. The sulfites are there to prevent oxidation, and minor oxidation in a white is a far more obvious fault -- visually, and on the nose -- than in a red. People nowadays expect their whites to be crisp and fruity and without a hint of oxidation.

Especially lots of sulfites in off-dry whites, which require a lot more intervention to stop them from fermenting to dry (sterile filtration, extra sulfite, and sometimes potassium sorbate [which I can personally taste at even extremely low concentrations and instantly classifies the wine as 'cheap' to me])

Finally, should mention that while sulfites are added, they also occur naturally as a byproduct of fermentation. Yeasts produce them. Another way (along with alcohol production) they they seem to want to commit suicide :-)

One thing that is (mostly) unique in reds is malolactic fermentation / malolactic bacteria. I've always wondered if the red-wine-headache people might in fact be sensitive to byproducts from that.