I've made numerous sail trips to St Croix over the past several years. I've never felt unsafe but here are some suggestions:
Avoid Buck Island and Christiansted Harbor on Sundays when the local go-fast boats show up.
If renting a vehicle and leaving it parked to do a beach excursion or hike, take all your valuables and leave the vehicle unlocked. In one day I saw vehicles broken into at the Isaac & Jack Bay trail head and at the West Beach parking lot south of Frederiksted.