The article headline and content is incredibly misleading. The governor didn't veto the bill, his office expressed disapproval but it was tabled in committee. The bill didn't have anything to do with warrants specifically seeking menstrual data - no such warrants exist. Basically, the bill would carve out menstrual tracking apps (e.g. Flo, Clue) as EXCLUDED from phone data that could be collected during a warrant.

If the police have a warrant to search your phone for child pornography, or planning to commit murder, etc, they could search every single file on the phone, every app. This bill would specifically carve out menstrual data from that, a protection which does not exist for any other app. Not for your bank app, or your email app, or your Tindr, whatever.

As a Democrat Virginian who has been following this for a while: the bill was signalling from Democrat legislators that they care about defending reproductive choice in the wake of Roe V. Wade overturn, but never had any practical reason to become law. The menstrual app on your phone is not protected by HIPAA, it's not protected records from a healthcare provider. It's the same as if the police have a warrant to search your house and you have a notebook where you have written with pen in which you record your cycle. They can still seize it during the search.