It's around 15% exported in the American west and 4% nation wide. That's not nothing, but it's mostly for domestic consumption, the headlines about it are kind of misleading by making it sound like a majority

Alfalfa is the third largest economic product in the US, but only 4% is exported annually. In the western states, however, which are high producers close to shipping ports to major export markets like China, Saudi Arabia and Japan, about 15% is exported each year

https://www.theguardian.com/us-news/2019/mar/25/california-water-drought-scarce-saudi-arabia