Sperm banks have been around for decades, but the advent in the past several years of low-cost chemical preservatives administered at home, which can extend the life of a sample for days, lowered the barriers to access by eliminating the awkward trip to a clinic or doctor’s office. Changing attitudes among health-conscious men are helping create a mini industry of direct-to-consumer startups that take semen by mail for storage and offer reproductive health analysis through an app.